# GRE Subject Test: Math : Vectors & Spaces

## Example Questions

### Example Question #18 : Vector

What is the vector form of ?

None of the above

Explanation:

Given , we need to map the , and  coefficients back to their corresponding , and -coordinates.

Thus the vector form of  is

.

### Example Question #41 : Linear Algebra

What is the vector form of ?

None of the above

Explanation:

Given , we need to map the , and  coefficients back to their corresponding , and -coordinates.

Thus the vector form of  is

.

### Example Question #11 : Vector

What is the dot product of  and ?

Explanation:

The dot product of two vectors is the sum of the products of the vectors' corresponding elements. Given  and , then:

### Example Question #21 : Vector

What is the dot product of  and ?

Explanation:

The dot product of two vectors is the sum of the products of the vectors' corresponding elements. Given  and , then:

### Example Question #22 : Vector

What is the dot product of  and ?

Explanation:

The dot product of two vectors is the sum of the products of the vectors' corresponding elements. Given  and , then:

### Example Question #41 : Linear Algebra

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 #42 : Linear Algebra

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 #43 : Linear Algebra

What is the vector form of ?

None of the above

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 #44 : Linear Algebra

What is the vector form of ?

Explanation:

In order to derive the vector form, we must map the vector elements to their corresponding , , and coefficients. That is, given, the vector form is  . So for , we can derive the vector form .

### Example Question #42 : Linear Algebra

What is the vector form of ?