### All GRE Subject Test: Math Resources

## Example Questions

### Example Question #58 : Vector

What is the vector form of ?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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

?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

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

**Correct answer:**

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

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 ?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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 .

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