# GRE Subject Test: Math : Vectors & Spaces

## Example Questions

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### Example Question #91 : Vectors & Spaces

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 .

### Example Question #89 : Vector

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 .

### Example Question #90 : Vector

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:

### Example Question #91 : Vector Form

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 .

### Example Question #92 : Vector Form

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 .

### Example Question #93 : Vector Form

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:

### Example Question #94 : Vector Form

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:

### Example Question #95 : Vector Form

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 .

### Example Question #96 : Vector Form

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 .

### Example Question #92 : Vectors & Spaces

Calculate the dot product of the following vectors: