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Common Core: High School - Number and Quantity : Vector & Matrix Quantities

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

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All Common Core: High School - Number and Quantity Resources

6 Diagnostic Tests 49 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

If v=<-3,4> $\displaystyle v=< -3,4>$, and w=<2,3> $\displaystyle w=< 2,3>$, what is v-w $\displaystyle v-w$?

Possible Answers:

v-w=<-5,-1> $\displaystyle v-w=< -5,-1>$

v-w=<1,-5> $\displaystyle v-w=< 1,-5>$

v-w=<5,-1> $\displaystyle v-w=< 5,-1>$

v-w=<5,1> $\displaystyle v-w=< 5,1>$

v-w=<-5,1> $\displaystyle v-w=< -5,1>$

Correct answer:

v-w=<-5,1> $\displaystyle v-w=< -5,1>$

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components.

$x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$ $\displaystyle x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$

$y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$ $\displaystyle y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$

$(x\: \mbox{component in}\: v)=-3$ $\displaystyle (x\: \mbox{component in}\: v)=-3$

$(x\:\mbox{component in}\: w)=2$ $\displaystyle (x\:\mbox{component in}\: w)=2$

$(y\: \mbox{component in}\: v)=4$ $\displaystyle (y\: \mbox{component in}\: v)=4$

$(y\: \mbox{component in}\: w)=3$ $\displaystyle (y\: \mbox{component in}\: w)=3$

$\displaystyle x=-3-2=-5$

y=4-3=1 $\displaystyle y=4-3=1$

So our final answer is <-5,1> $\displaystyle < -5,1>$.

Below is a visual representation.

Vecsub

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Example Question #2 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

If v=<4,-2> $\displaystyle v=< 4,-2>$, and w=<4,3> $\displaystyle w=< 4,3>$, what is v-w $\displaystyle v-w$?

Possible Answers:

v-w=<0,5> $\displaystyle v-w=< 0,5>$

v-w=<0,-5> $\displaystyle v-w=< 0,-5>$

v-w=<-5,0> $\displaystyle v-w=< -5,0>$

v-w=<5,0> $\displaystyle v-w=< 5,0>$

v-w=<8,1> $\displaystyle v-w=< 8,1>$

Correct answer:

v-w=<0,-5> $\displaystyle v-w=< 0,-5>$

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components.

$x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$ $\displaystyle x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$

$y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$ $\displaystyle y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$

$(x\: \mbox{component in}\: v)=4$ $\displaystyle (x\: \mbox{component in}\: v)=4$

$(x\:\mbox{component in}\: w)=4$ $\displaystyle (x\:\mbox{component in}\: w)=4$

$(y\: \mbox{component in}\: v)=-2$ $\displaystyle (y\: \mbox{component in}\: v)=-2$

$(y\: \mbox{component in}\: w)=3$ $\displaystyle (y\: \mbox{component in}\: w)=3$

x=4-4=0 $\displaystyle x=4-4=0$

$\displaystyle y=-2-3=-5$

So our final answer is <0,-5> $\displaystyle < 0,-5>$.

Below is a visual representation.

Screen shot 2016 03 08 at 9.31.39 am

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Example Question #3 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

If v=<-10,5> $\displaystyle v=< -10,5>$, and w=<-6,-7> $\displaystyle w=< -6,-7>$, what is v-w $\displaystyle v-w$?

Possible Answers:

v-w=<12,4> $\displaystyle v-w=< 12,4>$

v-w=<-4,12> $\displaystyle v-w=< -4,12>$

v-w=<-16,2> $\displaystyle v-w=< -16,2>$

v-w=<12,-4> $\displaystyle v-w=< 12,-4>$

v-w=<4,12> $\displaystyle v-w=< 4,12>$

Correct answer:

v-w=<-4,12> $\displaystyle v-w=< -4,12>$

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components.

$x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$ $\displaystyle x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$

$y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$ $\displaystyle y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$

$(x\: \mbox{component in}\: v)=-10$ $\displaystyle (x\: \mbox{component in}\: v)=-10$

$(x\:\mbox{component in}\: w)=-6$ $\displaystyle (x\:\mbox{component in}\: w)=-6$

$(y\: \mbox{component in}\: v)=5$ $\displaystyle (y\: \mbox{component in}\: v)=5$

$(y\: \mbox{component in}\: w)=-7$ $\displaystyle (y\: \mbox{component in}\: w)=-7$

$\displaystyle x=-10-(-6)=-10+6=-4$

$\displaystyle y=5-(-7)=5+7=12$

So our final answer is <-4,12> $\displaystyle < -4,12>$.

Below is a visual representation.

Screen shot 2016 03 08 at 9.52.05 am

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Example Question #4 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

If v=<1,1> $\displaystyle v=< 1,1>$, and w=<-7,-9> $\displaystyle w=< -7,-9>$, what is v-w $\displaystyle v-w$?

Possible Answers:

v-w=<8,-10> $\displaystyle v-w=< 8,-10>$

v-w=<8,10> $\displaystyle v-w=< 8,10>$

v-w=<10,8> $\displaystyle v-w=< 10,8>$

v-w=<-8,10> $\displaystyle v-w=< -8,10>$

v-w=<-10,-8> $\displaystyle v-w=< -10,-8>$

Correct answer:

v-w=<8,10> $\displaystyle v-w=< 8,10>$

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components.

$x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$ $\displaystyle x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$

$y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$ $\displaystyle y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$

$(x\: \mbox{component in}\: v)=1$ $\displaystyle (x\: \mbox{component in}\: v)=1$

$(x\:\mbox{component in}\: w)=-7$ $\displaystyle (x\:\mbox{component in}\: w)=-7$

$(y\: \mbox{component in}\: v)=1$ $\displaystyle (y\: \mbox{component in}\: v)=1$

$(y\: \mbox{component in}\: w)=-9$ $\displaystyle (y\: \mbox{component in}\: w)=-9$

$\displaystyle x=1-(-7)=1+7=8$

$\displaystyle y=1-(-9)=1+9=10$

So our final answer is <8,10> $\displaystyle < 8,10>$.

Below is a visual representation.

Screen shot 2016 03 08 at 10.22.33 am

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Example Question #5 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

If v=<-2,-2> $\displaystyle v=< -2,-2>$, and w=<-1,-4> $\displaystyle w=< -1,-4>$, what is v-w $\displaystyle v-w$?

Possible Answers:

<-2,-1> $\displaystyle < -2,-1>$

<2,1> $\displaystyle < 2,1>$

<-1,2> $\displaystyle < -1,2>$

<1,-2> $\displaystyle < 1,-2>$

<-6,-1> $\displaystyle < -6,-1>$

Correct answer:

<-1,2> $\displaystyle < -1,2>$

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components.

$x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$ $\displaystyle x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$

$y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$ $\displaystyle y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$

$(x\: \mbox{component in}\: v)=-2$ $\displaystyle (x\: \mbox{component in}\: v)=-2$

$(x\:\mbox{component in}\: w)=-1$ $\displaystyle (x\:\mbox{component in}\: w)=-1$

$(y\: \mbox{component in}\: v)=-2$ $\displaystyle (y\: \mbox{component in}\: v)=-2$

$(y\: \mbox{component in}\: w)=-4$ $\displaystyle (y\: \mbox{component in}\: w)=-4$

$\displaystyle x=-2-(-1)=-2+1=-1$

$\displaystyle y=-2-(-4)=-2+4=2$

So our final answer is <-1,2> $\displaystyle < -1,2>$.

Below is a visual representation.

Screen shot 2016 03 10 at 12.55.41 pm

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Example Question #6 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

If v=<-10,-1> $\displaystyle v=< -10,-1>$, and w=<-9,-7> $\displaystyle w=< -9,-7>$, what is v-w $\displaystyle v-w$?

Possible Answers:

<-1,6> $\displaystyle < -1,6>$

<6, -1> $\displaystyle < 6, -1>$

<-1,-6> $\displaystyle < -1,-6>$

<1,6> $\displaystyle < 1,6>$

<1,-6> $\displaystyle < 1,-6>$

Correct answer:

<-1,6> $\displaystyle < -1,6>$

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components.

$x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$ $\displaystyle x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$

$y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$ $\displaystyle y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$

$(x\: \mbox{component in}\: v)=-10$ $\displaystyle (x\: \mbox{component in}\: v)=-10$

$(x\:\mbox{component in}\: w)=-9$ $\displaystyle (x\:\mbox{component in}\: w)=-9$

$(y\: \mbox{component in}\: v)=-1$ $\displaystyle (y\: \mbox{component in}\: v)=-1$

$(y\: \mbox{component in}\: w)=-7$ $\displaystyle (y\: \mbox{component in}\: w)=-7$

$\displaystyle x=-10-(-9)=-10+9=-1$

$\displaystyle y=-1-(-7)=-1+7=6$

So our final answer is <-1,6> $\displaystyle < -1,6>$.

Below is a visual representation.

Screen shot 2016 03 10 at 1.03.06 pm

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Example Question #1 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

If v=<-9,-9> $\displaystyle v=< -9,-9>$, and w=<-4,11> $\displaystyle w=< -4,11>$, what is v-w $\displaystyle v-w$?

Possible Answers:

<-5,-20> $\displaystyle < -5,-20>$

<-13,-20> $\displaystyle < -13,-20>$

<13,-20> $\displaystyle < 13,-20>$

<5,-20> $\displaystyle < 5,-20>$

<13,20> $\displaystyle < 13,20>$

Correct answer:

<-5,-20> $\displaystyle < -5,-20>$

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components.

$x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$ $\displaystyle x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$

$y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$ $\displaystyle y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$

$(x\: \mbox{component in}\: v)=-9$ $\displaystyle (x\: \mbox{component in}\: v)=-9$

$(x\:\mbox{component in}\: w)=-4$ $\displaystyle (x\:\mbox{component in}\: w)=-4$

$(y\: \mbox{component in}\: v)=-9$ $\displaystyle (y\: \mbox{component in}\: v)=-9$

$(y\: \mbox{component in}\: w)=11$ $\displaystyle (y\: \mbox{component in}\: w)=11$

$\displaystyle x=-9-(-4)=-9+4=-5$

$\displaystyle y=-9-11=-20$

So our final answer is <-5,-20> $\displaystyle < -5,-20>$.

Below is a visual representation.

Screen shot 2016 03 10 at 1.09.46 pm

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Example Question #8 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

If v=<-8,-10> $\displaystyle v=< -8,-10>$, and w=<4,14> $\displaystyle w=< 4,14>$, what is v-w $\displaystyle v-w$?

Possible Answers:

<24,-12> $\displaystyle < 24,-12>$

<-12,-24> $\displaystyle < -12,-24>$

<-12,24> $\displaystyle < -12,24>$

<-24,-12> $\displaystyle < -24,-12>$

<-24,12> $\displaystyle < -24,12>$

Correct answer:

<-12,-24> $\displaystyle < -12,-24>$

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components.

$x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$ $\displaystyle x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$

$y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$ $\displaystyle y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$

$(x\: \mbox{component in}\: v)=-8$ $\displaystyle (x\: \mbox{component in}\: v)=-8$

$(x\:\mbox{component in}\: w)=4$ $\displaystyle (x\:\mbox{component in}\: w)=4$

$(y\: \mbox{component in}\: v)=-10$ $\displaystyle (y\: \mbox{component in}\: v)=-10$

$(y\: \mbox{component in}\: w)=14$ $\displaystyle (y\: \mbox{component in}\: w)=14$

$\displaystyle x=-8-4=-12$

$\displaystyle y=-10-14=-24$

So our final answer is <-12,-24> $\displaystyle < -12,-24>$.

Below is a visual representation.

Screen shot 2016 03 10 at 1.16.09 pm

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Example Question #1 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

If v=<-15,1> $\displaystyle v=< -15,1>$, and w=<-2,3> $\displaystyle w=< -2,3>$, what is v-w $\displaystyle v-w$?

Possible Answers:

<-13,3> $\displaystyle < -13,3>$

<13,-2> $\displaystyle < 13,-2>$

<-1,-2> $\displaystyle < -1,-2>$

<-13,-2> $\displaystyle < -13,-2>$

<-17,3> $\displaystyle < -17,3>$

Correct answer:

<-13,-2> $\displaystyle < -13,-2>$

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components.

$x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$ $\displaystyle x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$

$y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$ $\displaystyle y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$

$(x\: \mbox{component in}\: v)=-15$ $\displaystyle (x\: \mbox{component in}\: v)=-15$

$(x\:\mbox{component in}\: w)=-2$ $\displaystyle (x\:\mbox{component in}\: w)=-2$

$(y\: \mbox{component in}\: v)=1$ $\displaystyle (y\: \mbox{component in}\: v)=1$

$(y\: \mbox{component in}\: w)=3$ $\displaystyle (y\: \mbox{component in}\: w)=3$

$\displaystyle x=-15-(-2)=-15+2=-13$

$\displaystyle y=1-3=-2$

So our final answer is <-13,-2> $\displaystyle < -13,-2>$.

Below is a visual representation.

Screen shot 2016 03 10 at 1.25.04 pm

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Example Question #2 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

If v=<3,4> $\displaystyle v=< 3,4>$, and w=<-3,-12> $\displaystyle w=< -3,-12>$, what is v-w $\displaystyle v-w$?

Possible Answers:

<0,8> $\displaystyle < 0,8>$

<6,16> $\displaystyle < 6,16>$

<16,6> $\displaystyle < 16,6>$

<0,-8> $\displaystyle < 0,-8>$

<6,-16> $\displaystyle < 6,-16>$

Correct answer:

<6,16> $\displaystyle < 6,16>$

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components.

$x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$ $\displaystyle x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$

$y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$ $\displaystyle y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$

$(x\: \mbox{component in}\: v)=3$ $\displaystyle (x\: \mbox{component in}\: v)=3$

$(x\:\mbox{component in}\: w)=-3$ $\displaystyle (x\:\mbox{component in}\: w)=-3$

$(y\: \mbox{component in}\: v)=4$ $\displaystyle (y\: \mbox{component in}\: v)=4$

$(y\: \mbox{component in}\: w)=-12$ $\displaystyle (y\: \mbox{component in}\: w)=-12$

$\displaystyle x=3-(-3)=3+3=6$

$\displaystyle y=4-(-12)=4+12=16$

So our final answer is <6,16> $\displaystyle < 6,16>$.

Below is a visual representation.

Screen shot 2016 03 10 at 1.38.47 pm

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Common Core: High School - Number and Quantity : Vector & Matrix Quantities

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

All Common Core: High School - Number and Quantity Resources

Example Questions

Example Question #1 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

Example Question #2 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

Example Question #3 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

Example Question #4 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

Example Question #5 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

Example Question #6 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

Example Question #1 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

Example Question #8 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

Example Question #1 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

Example Question #2 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

All Common Core: High School - Number and Quantity Resources

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