# GRE Subject Test: Math : Vectors & Spaces

## Example Questions

### Example Question #51 : 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 #52 : 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 #53 : Vectors & Spaces

Write the following parametric equation in vector form.

Explanation:

When converting parametric equations to vector valued functions, remember that the order of vectors goes as follows.

Given the question

the vector would be given as,

.

### Example Question #54 : 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 #55 : 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 #56 : 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 #57 : Vectors & Spaces

Find the vector in standard form if the initial point is located at  and the terminal point is located at .

Explanation:

We must first find the vector in component form.

If the initial point is  and the terminal point is  then the component form of the vector is .

As such, the component form of the vector in the problem is

Next, any vector with component form  can be written in standard form as   .

Hence, the vector in standard form is

### Example Question #58 : 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 #59 : 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 #60 : Vectors & Spaces

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: