# GRE Subject Test: Math : Vectors & Spaces

## Example Questions

### Example Question #81 : Vectors & Spaces

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

Possible Answers:

Correct answer:

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:

### Example Question #82 : Vectors & Spaces

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

Possible Answers:

Correct answer:

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:

### Example Question #83 : Vectors & Spaces

What is the vector form of ?

Possible Answers:

Correct answer:

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 .

### Example Question #84 : Vectors & Spaces

What is the vector form of ?

Possible Answers:

Correct answer:

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 .

### Example Question #85 : Vectors & Spaces

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

Possible Answers:

Correct answer:

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:

### Example Question #86 : Vectors & Spaces

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

Possible Answers:

Correct answer:

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:

### Example Question #87 : Vectors & Spaces

What is the vector form of ?

Possible Answers:

Correct answer:

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 .

### Example Question #88 : Vectors & Spaces

What is the vector form of ?

Possible Answers:

Correct answer:

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 .

### Example Question #89 : Vectors & Spaces

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

Possible Answers:

Correct answer:

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:

### Example Question #90 : Vectors & Spaces

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

Possible Answers:

Correct answer:

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: