Vector Subtraction as the Additive Inverse: CCSS.Math.Content.HSN-VM.B.4c

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Common Core: High School - Number and Quantity › Vector Subtraction as the Additive Inverse: CCSS.Math.Content.HSN-VM.B.4c

Questions 1 - 10

If , and , what is ?

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.

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

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

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

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

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

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

So our final answer is .

Below is a visual representation.

Screen shot 2016 03 10 at 1.25.04 pm

If , and , what is ?

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.

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

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

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

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

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

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

So our final answer is .

Below is a visual representation.

Screen shot 2016 03 10 at 2.06.50 pm

If , and , what is ?

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.

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

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

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

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

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

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

So our final answer is .

Below is a visual representation.

Screen shot 2016 03 08 at 9.52.05 am

If , and , what is ?

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.

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

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

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

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

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

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

So our final answer is .

Below is a visual representation.

Screen shot 2016 03 08 at 9.31.39 am

If , and , what is ?

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.

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

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

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

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

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

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

So our final answer is .

Below is a visual representation.

Screen shot 2016 03 10 at 12.55.41 pm

If , and , what is ?

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.

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

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

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

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

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

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

So our final answer is .

Below is a visual representation.

Vecsub

If , and , what is ?

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.

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

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

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

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

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

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

So our final answer is .

Below is a visual representation.

Screen shot 2016 03 08 at 10.22.33 am

If , and , what is ?

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.

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

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

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

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

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

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

So our final answer is .

Below is a visual representation.

Screen shot 2016 03 10 at 1.16.09 pm

If , and , what is ?

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.

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

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

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

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

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

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

So our final answer is .

Below is a visual representation.

Screen shot 2016 03 10 at 2.13.54 pm

If , and , what is ?

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.

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

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

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

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

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

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

So our final answer is .

Below is a visual representation.

Screen shot 2016 03 10 at 1.09.46 pm

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