# GRE Subject Test: Math : Vectors

## Example Questions

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### Example Question #1 : Vectors & Spaces

Calculate the dot product of the following vectors:

Explanation:

Write the formula for dot product given  and .

Substitute the values of the vectors to determine the dot product.

### Example Question #2 : Vectors & Spaces

Express  in vector form.

Explanation:

The correct form of x,y, and z of a vector is represented in the order of i, j, and k, respectively. The coefficients of i,j, and k are used to write the vector form.

### Example Question #3 : Vectors & Spaces

Express  in vector form.

Explanation:

The x,y, and z of a vector is represented in the order of i, j, and k, respectively. Use the coefficients of i,j, and k to write the vector form.

### Example Question #1 : Vector Form

Find the vector form of  to .

Explanation:

When we are trying to find the vector form we need to remember the formula which states to take the difference between the ending and starting point.

Thus we would get:

Given  and

In our case we have ending point at  and our starting point at .

Therefore we would set up the following and simplify.

### Example Question #1 : Vector Form

Find the dot product of the 2 vectors.

Explanation:

The dot product will give a single value answer, and not a vector as a result.

To find the dot product, use the following formula:

### Example Question #6 : Vectors & Spaces

Assume that Billy fired himself out of a circus cannon at a velocity of  at an elevation angle of  degrees.  Write this in vector component form.

Explanation:

The firing of the cannon has both x and y components.

Write the formula that distinguishes the x and y direction and substitute.

Ensure that the calculator is in degree mode before you solve.

### Example Question #7 : Vectors & Spaces

Compute:   given the following vectors.   and .

Explanation:

The dimensions of the vectors are mismatched.

Since vector  does not have the same dimensions as , the answer for  cannot be solved.

### Example Question #8 : Vectors & Spaces

What is the vector form of ?

Explanation:

To find the vector form of , we must map the coefficients of , and  to their corresponding , and  coordinates. Thus,  becomes .

### Example Question #9 : Vectors & Spaces

Express  in vector form.

Explanation:

In order to express  in vector form, we must use the coefficients of and  to represent the -, -, and -coordinates of the vector.

Therefore, its vector form is

.

### Example Question #1 : Vector Form

Express  in vector form.