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Common Core: High School - Number and Quantity : Vector Components: CCSS.Math.Content.HSN-VM.A.2

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Example Questions

Example Question #1 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

What are the components of a vector that has a terminal point of (5,10) , and an initial point of (2,3) ?

Possible Answers:

<7,3>

<3.5, -3>

<3,7>

<-3,-7>

<0,0>

Correct answer:

<3,7>

Explanation:

In order to determine what the components of this vector has, we need to remember how to find components of a vector. It's simply the difference between the terminal point and initial point. The first step is to write an equation for what our "new" x and y are.

$x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\\ \mbox{(x in terminal point)}=5 \\ \mbox{(x in initial point)}=2 \\ \mbox{(y in terminal point)}=10\\ \mbox{(y in initial point)}= 3$

x=5-2=3

y=10-3=7

To write this in component form, we need to put our , and into .

So the final answer is <3,7>

Below is a visual representation of what we just did.

Term

The blue line is our original vector, and the red line is the same vector, but begins at the origin rather than at the initial point.

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Example Question #2 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

What are the components of a vector that has a terminal point of (5,-10) , and an initial point of (-2,3) ?

Possible Answers:

<-13,7>

<-13,-7>

<7,-13>

<-7,13>

<13,7>

Correct answer:

<7,-13>

Explanation:

n order to determine what the components of this vector has, we need to remember how to find components of a vector. It's simply the difference between the terminal point and initial point. The first step is to write an equation for what our "new" x and y are.

$x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\\ \mbox{(x in terminal point)}=5 \\ \mbox{(x in initial point)}=-2 \\ \mbox{(y in terminal point)}=-10\\ \mbox{(y in initial point)}= 3$

x=5-(-2)=7

y=-10-3=-13

To write this in component form, we need to put our , and into .

So the final answer is <7,-13>

Below is a visual representation of what we just did.

Comp2

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Example Question #11 : Vector & Matrix Quantities

What are the components of a vector that has a terminal point of (1,1) , and an initial point of (-6,-9) ?

Possible Answers:

<0,0>

<7,10>

<-10,-7>

<-7,-10>

<10,7>

Correct answer:

<7,10>

Explanation:

$x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\\ \mbox{(x in terminal point)}=1 \\ \mbox{(x in initial point)}=-6 \\ \mbox{(y in terminal point)}=1\\ \mbox{(y in initial point)}= -9$

x=1-(-6)=1+6=7

y=1-(-9)=1+9=10

To write this in component form, we need to put our , and into .

So the final answer is <7,10>

Below is a visual representation of what we just did.

Screen shot 2016 03 15 at 10.39.47 am

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Example Question #12 : Vector & Matrix Quantities

What are the components of a vector that has a terminal point of (-9,1) , and an initial point of (5,-10) ?

Possible Answers:

<-14,11>

<14,-11>

<11,-14>

<11,14>

<-14,-11>

Correct answer:

<-14,11>

Explanation:

$x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\\ \mbox{(x in terminal point)}=-9 \\ \mbox{(x in initial point)}=2 \\ \mbox{(y in terminal point)}=1\\ \mbox{(y in initial point)}= -10$

x=-9-5=-14

y=1-(-10)=1+10=11

To write this in component form, we need to put our , and into .

So the final answer is <-14,11>

Below is a visual representation of what we just did.

Screen shot 2016 03 15 at 10.52.08 am

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Example Question #113 : High School: Number And Quantity

What are the components of a vector that has a terminal point of (3,-8) , and an initial point of (6,-13) ?

Possible Answers:

<-21,9>

<9,-21>

<-3,5>

<5,-3>

<-5,-7>

Correct answer:

<-3,5>

Explanation:

$x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\\ \mbox{(x in terminal point)}=3 \\ \mbox{(x in initial point)}=6 \\ \mbox{(y in terminal point)}=-8\\ \mbox{(y in initial point)}= -13$

x=3-6=-3

y=-8-(-13)=-8+13=5

To write this in component form, we need to put our , and into .

So the final answer is <-3,5>

Below is a visual representation of what we just did.

Screen shot 2016 03 15 at 12.32.48 pm

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Example Question #114 : High School: Number And Quantity

What are the components of a vector that has a terminal point of (-1,-5) , and an initial point of (-4,-9) ?

Possible Answers:

<-4,3>

<8,-1>

<4,5>

<4,3>

<3,4>

Correct answer:

<3,4>

Explanation:

$x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\\ \mbox{(x in terminal point)}=-1 \\ \mbox{(x in initial point)}=-4 \\ \mbox{(y in terminal point)}=-5\\ \mbox{(y in initial point)}= -9$

x=-1-(-4)=-1+4=3

y=-5-(-9)=-5+9=4

To write this in component form, we need to put our , and into .

So the final answer is <3,4>

Below is a visual representation of what we just did.

Screen shot 2016 03 16 at 12.09.51 pm

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Example Question #3 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

What are the components of a vector that has a terminal point of (-3,10) , and an initial point of (-4,12) ?

Possible Answers:

<1,2>

<-2,1>

<1,-2>

<-15,14>

<14,-15>

Correct answer:

<1,-2>

Explanation:

$x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\\ \mbox{(x in terminal point)}=-3 \\ \mbox{(x in initial point)}=-4 \\ \mbox{(y in terminal point)}=10\\ \mbox{(y in initial point)}=12$

x=-3-(-4)=-3+4=1

y=10-12=-2

To write this in component form, we need to put our , and into .

So the final answer is <1,-2>

Below is a visual representation of what we just did.

Screen shot 2016 03 16 at 12.32.22 pm

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Example Question #4 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

What are the components of a vector that has a terminal point of (1,9) , and an initial point of (-7,5) ?

Possible Answers:

<8,4>

<8,14>

<4,-6>

<-6,4>

<4,6>

Correct answer:

<8,4>

Explanation:

$x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\\ \mbox{(x in terminal point)}=1 \\ \mbox{(x in initial point)}=-7 \\ \mbox{(y in terminal point)}=9\\ \mbox{(y in initial point)}= 5$

x=1-(-7)=1+7=8

y=9-5=4

To write this in component form, we need to put our , and into .

So the final answer is <8,4>

Below is a visual representation of what we just did.

Screen shot 2016 03 16 at 12.41.19 pm

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Example Question #1 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

What are the components of a vector that has a terminal point of (4,6) , and an initial point of (0,-8) ?

Possible Answers:

<6,12>

<-2,8>

<12,6>

<14,4>

<4,14>

Correct answer:

<4,14>

Explanation:

$x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\\ \mbox{(x in terminal point)}=4 \\ \mbox{(x in initial point)}=0 \\ \mbox{(y in terminal point)}=6\\ \mbox{(y in initial point)}= -8$

x=4-0=4

y=6-(-8)=6+8=14

To write this in component form, we need to put our , and into .

So the final answer is <4,14>

Below is a visual representation of what we just did.

Screen shot 2016 03 16 at 1.16.38 pm

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Example Question #5 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

What are the components of a vector that has a terminal point of (3,-6) , and an initial point of (10,5) ?

Possible Answers:

<-11,-7>

<-7,-11>

<-8,4>

<8,4>

<8,-4>

Correct answer:

<-7,-11>

Explanation:

$x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\\ \mbox{(x in terminal point)}=3 \\ \mbox{(x in initial point)}=10 \\ \mbox{(y in terminal point)}=-6\\ \mbox{(y in initial point)}=5$

x=3-10=-7

y=-6-5=-11

To write this in component form, we need to put our , and into .

So the final answer is <-7,-11>

Below is a visual representation of what we just did.

Screen shot 2016 03 16 at 1.27.32 pm

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Common Core: High School - Number and Quantity : Vector Components: CCSS.Math.Content.HSN-VM.A.2

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 Components: Ccss.Math.Content.Hsn Vm.A.2

Example Question #2 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

Example Question #11 : Vector & Matrix Quantities

Example Question #12 : Vector & Matrix Quantities

Example Question #113 : High School: Number And Quantity

Example Question #114 : High School: Number And Quantity

Example Question #3 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

Example Question #4 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

Example Question #1 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

Example Question #5 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

All Common Core: High School - Number and Quantity Resources

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