Vectors

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GRE Quantitative Reasoning › Vectors

Questions 1 - 10
1

What is the vector form of ?

Explanation

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients.

That is, given , the vector form is .

So for , we can derive the vector form .

2

Given points and , what is the vector form of the distance between the points?

Explanation

In order to derive the vector form of the distance between two points, we must find the difference between the , , and elements of the points. That is, for any point and , the distance is the vector .

Subbing in our original points and , we get:

3

What is the vector form of ?

Explanation

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients.

That is, given, the vector form is .

So for , we can derive the vector form .

4

What is the vector form of ?

Explanation

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients.

That is, given, the vector form is .

So for , we can derive the vector form .

5

What is the vector form of ?

Explanation

Given , we need to map the , , and coefficients back to their corresponding , , and -coordinates.

Thus the vector form of is

.

6

What is the vector form of ?

None of the above

Explanation

In order to derive the vector form, we must map the vector elements to their corresponding , , and coefficients. That is, given , the vector form is . So for , we can derive the vector form .

7

What is the vector form of ?

Explanation

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients.

That is, given, the vector form is .

So for , we can derive the vector form .

8

What is the vector form of ?

Explanation

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients. That is, given, the vector form is . So for , we can derive the vector form .

9

Given points and , what is the vector form of the distance between the points?

Explanation

In order to derive the vector form of the distance between two points, we must find the difference between the , , and elements of the points. That is, for any point and , the distance is the vector .

Subbing in our original points and , we get:

10

What is the vector form of ?

None of the above

Explanation

To find the vector form of , we must map the coefficients of , , and to their corresponding , , and coordinates.

Thus, becomes .

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