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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

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Example Questions

Example Question #71 : Vector & Matrix Quantities

If v=<10,-10> , and w=<4,-14> , what is v-w ?

Possible Answers:

<-14,-24>

<6,4>

<14,-24>

<14,24>

<4,6>

Correct answer:

<6,4>

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.

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

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

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

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

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

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

x=10-4=6

y=-10-(-14)=-10+14=4

So our final answer is <6,4> .

Below is a visual representation.

Screen shot 2016 03 10 at 2.06.50 pm

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Example Question #72 : Vector & Matrix Quantities

If v=<2,0> , and w=<5,-1> , what is v-w ?

Possible Answers:

<1,-3>

<-3,1>

<3,-1>

<-3,-1>

<3,1>

Correct answer:

<-3,1>

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.

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

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

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

$(x\:\mbox{component in}\: w)=5$

$(y\: \mbox{component in}\: v)=0$

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

x=2-5=-3

y=0-(-1)=0+1=1

So our final answer is <-3,1> .

Below is a visual representation.

Screen shot 2016 03 10 at 2.13.54 pm

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Example Question #1 : Represent Scalar Multiplication Graphically: Ccss.Math.Content.Hsn Vm.B.5a

If v=<-3,7> , what is ?

Possible Answers:

6v=<-3,13>

6v=<-18,42>

6v=<-18,-42>

6v=<18,-42>

6v=<18,42>

Correct answer:

6v=<-18,42>

Explanation:

Multiplying a vector by a scalar is as simple as multiplying the scalar by each vector component. In equation form it looks like this.

$x=k\cdot(x\: \mbox{component})$

$y=k\cdot(y\: \mbox{component})$

where is the scalar.

In this case it is

$x=6\cdot-3=-18$

$y=6\cdot7=42$

The final answer is then <-18,42> .

There is a visual representation below.

The solid red arrow is , and the dashed blue line is .

Multscalar

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Example Question #1 : Represent Scalar Multiplication Graphically: Ccss.Math.Content.Hsn Vm.B.5a

If v=<-8,0> , what is ?

Possible Answers:

4v=<32,0>

4v=<0,32>

4v=<0,-32>

4v=<-32,0>

4v=<0,3>

Correct answer:

4v=<-32,0>

Explanation:

Multiplying a vector by a scalar is as simple as multiplying the scalar by each vector component. In equation form it looks like this.

$x=k\cdot(x\: \mbox{component})$

$y=k\cdot(y\: \mbox{component})$

where is the scalar.

In this case it is

$x=-8\cdot4=-32$

$y=0\cdot4=0$

The final answer is then <-32,0> .

There is a visual representation below.

The solid red arrow is , and the dashed blue line is .

Screen shot 2016 03 07 at 1.19.53 pm

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Example Question #2 : Represent Scalar Multiplication Graphically: Ccss.Math.Content.Hsn Vm.B.5a

If v=<1,7> , what is -9v ?

Possible Answers:

-9v=<-9,-63>

-9v=<-63,-9>

-9v=<-9,63>

-9v=<9,63>

-9v=<9,-63>

Correct answer:

-9v=<-9,-63>

Explanation:

Multiplying a vector by a scalar is as simple as multiplying the scalar by each vector component. In equation form it looks like this.

$x=k\cdot(x\: \mbox{component})$

$y=k\cdot(y\: \mbox{component})$

where is the scalar.

In this case it is

$x=1\cdot-9=-9$

$y=7\cdot-9=-63$

The final answer is then <-9,-63> .

There is a visual representation below.

The solid red arrow is , and the dashed blue line is -9v .

Screen shot 2016 03 07 at 1.29.44 pm

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Example Question #3 : Represent Scalar Multiplication Graphically: Ccss.Math.Content.Hsn Vm.B.5a

If v=<5,10> , what is -11v ?

Possible Answers:

<-110, -55>

<-55,110>

<55,110>

<55,-110>

<-55,-110>

Correct answer:

<-55,-110>

Explanation:

Multiplying a vector by a scalar is as simple as multiplying the scalar by each vector component. In equation form it looks like this.

$x=k\cdot(x\: \mbox{component})$

$y=k\cdot(y\: \mbox{component})$

where is the scalar.

In this case it is

$x=5\cdot-11=-55$

$y=10\cdot-11=-110$

The final answer is then <-55,-110> .

There is a visual representation below.

The solid red arrow is , and the dashed blue line is -11v .

Screen shot 2016 03 07 at 2.51.12 pm

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Example Question #4 : Represent Scalar Multiplication Graphically: Ccss.Math.Content.Hsn Vm.B.5a

If v=<7,9> , what is ?

Possible Answers:

<56,72>

<72,56>

<-56,-72>

<-56,72>

<56,-72>

Correct answer:

<56,72>

Explanation:

Multiplying a vector by a scalar is as simple as multiplying the scalar by each vector component. In equation form it looks like this.

$x=k\cdot(x\: \mbox{component})$

$y=k\cdot(y\: \mbox{component})$

where is the scalar.

In this case it is

$x=7\cdot8=56$

$y=9\cdot8=72$

The final answer is then <56,72> .

There is a visual representation below.

The solid red arrow is , and the dashed blue line is .

Screen shot 2016 03 07 at 3.09.03 pm

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Example Question #5 : Represent Scalar Multiplication Graphically: Ccss.Math.Content.Hsn Vm.B.5a

If v=<-8,3> , what is 13v ?

Possible Answers:

<39,-104>

<-104,-39>

<-104,39>

<104,-39>

<104,39>

Correct answer:

<-104,39>

Explanation:

Multiplying a vector by a scalar is as simple as multiplying the scalar by each vector component. In equation form it looks like this.

$x=k\cdot(x\: \mbox{component})$

$y=k\cdot(y\: \mbox{component})$

where is the scalar.

In this case it is

$x=-8\cdot13=-104$

$y=3\cdot13=39$

The final answer is then <-104,39> .

There is a visual representation below.

The solid red arrow is , and the dashed blue line is 11v .

Screen shot 2016 03 07 at 3.16.13 pm

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Example Question #6 : Represent Scalar Multiplication Graphically: Ccss.Math.Content.Hsn Vm.B.5a

If v=<-3,-8> , what is ?

Possible Answers:

<3,8>

<8,3>

<-3,8>

<-3,-8>

<3,-8>

Correct answer:

<3,8>

Explanation:

Multiplying a vector by a scalar is as simple as multiplying the scalar by each vector component. In equation form it looks like this.

$x=k\cdot(x\: \mbox{component})$

$y=k\cdot(y\: \mbox{component})$

where is the scalar.

In this case it is

$x=-3\cdot-1=3$

$y=-8\cdot-1=8$

The final answer is then <3,8> .

There is a visual representation below.

The solid red arrow is , and the dashed blue line is .

Screen shot 2016 03 07 at 3.39.00 pm

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Example Question #7 : Represent Scalar Multiplication Graphically: Ccss.Math.Content.Hsn Vm.B.5a

If v=<0,5> , what is ?

Possible Answers:

<20,0>

<4,20>

<0,20>

<20,4>

<2,4>

Correct answer:

<0,20>

Explanation:

Multiplying a vector by a scalar is as simple as multiplying the scalar by each vector component. In equation form it looks like this.

$x=k\cdot(x\: \mbox{component})$

$y=k\cdot(y\: \mbox{component})$

where is the scalar.

In this case it is

$x=0\cdot4=0$

$y=5\cdot4=20$

The final answer is then <0,20> .

There is a visual representation below.

The solid red arrow is , and the dashed blue line is .

Screen shot 2016 03 07 at 3.43.53 pm

Report an Error

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All Common Core: High School - Number and Quantity Resources

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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 #71 : Vector & Matrix Quantities

Example Question #72 : Vector & Matrix Quantities

Example Question #1 : Represent Scalar Multiplication Graphically: Ccss.Math.Content.Hsn Vm.B.5a

Example Question #1 : Represent Scalar Multiplication Graphically: Ccss.Math.Content.Hsn Vm.B.5a

Example Question #2 : Represent Scalar Multiplication Graphically: Ccss.Math.Content.Hsn Vm.B.5a

Example Question #3 : Represent Scalar Multiplication Graphically: Ccss.Math.Content.Hsn Vm.B.5a

Example Question #4 : Represent Scalar Multiplication Graphically: Ccss.Math.Content.Hsn Vm.B.5a

Example Question #5 : Represent Scalar Multiplication Graphically: Ccss.Math.Content.Hsn Vm.B.5a

Example Question #6 : Represent Scalar Multiplication Graphically: Ccss.Math.Content.Hsn Vm.B.5a

Example Question #7 : Represent Scalar Multiplication Graphically: Ccss.Math.Content.Hsn Vm.B.5a

All Common Core: High School - Number and Quantity Resources

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