# GRE Subject Test: Math : Vectors & Spaces

## Example Questions

### Example Question #58 : 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 #59 : 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 #1 : 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 #441 : Gre Subject Test: Math

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 #62 : Vector

What is the derivative of the vector function

?

Explanation:

The derivative of a vector function has its components consisting of the derivatives of its components:

since the derivatives of  are , respectively.

### Example Question #81 : Linear Algebra

Given the vector function

what is the derivative of the vector function?

Explanation:

The derivative of a vector function is just the derivative of components:

The derivative of each component was found using the power rule which states,

.

Thus,

,

,

.

### Example Question #64 : Vector

What is not a way of describing the circle  in parametric form? Use the time interval .

All of the other answers describe the circle mentioned in the question.

All of the other answers describe the circle mentioned in the question.

Explanation:

All of the vector forms above describe the circle  since if we square their components and add them, we get (using trig. identities):

Therefore we get,

.

### Example Question #65 : 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 #66 : 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 #67 : 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 .