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

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Question

If , and , what is ?

Answer

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.

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Question

If , and , what is ?

Answer

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.

Compare your answer with the correct one above

Question

If , and , what is ?

Answer

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.

Compare your answer with the correct one above

Question

If , and , what is ?

Answer

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.

Compare your answer with the correct one above

Question

If , and , what is ?

Answer

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.

Compare your answer with the correct one above

Question

If , and , what is ?

Answer

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.

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

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

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

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

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

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

So our final answer is .

Below is a visual representation.

Compare your answer with the correct one above

Question

If , and , what is ?

Answer

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.

Compare your answer with the correct one above

Question

If , and , what is ?

Answer

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.

Compare your answer with the correct one above

Question

If , and , what is ?

Answer

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.

Compare your answer with the correct one above

Question

If , and , what is ?

Answer

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.

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

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

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

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

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

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

So our final answer is .

Below is a visual representation.

Compare your answer with the correct one above

Question

If , and , what is ?

Answer

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.

Compare your answer with the correct one above

Question

If , and , what is ?

Answer

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.

Compare your answer with the correct one above

Question

If , and , what is ?

Answer

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.

Compare your answer with the correct one above

Question

If , and , what is ?

Answer

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.

Compare your answer with the correct one above

Question

If , and , what is ?

Answer

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.

Compare your answer with the correct one above

Question

If , and , what is ?

Answer

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.

Compare your answer with the correct one above

Question

If , and , what is ?

Answer

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.

Compare your answer with the correct one above

Question

If , and , what is ?

Answer

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.

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

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

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

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

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

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

So our final answer is .

Below is a visual representation.

Compare your answer with the correct one above

Question

If , and , what is ?

Answer

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.

Compare your answer with the correct one above

Question

If , and , what is ?

Answer

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.

Compare your answer with the correct one above

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