### All GRE Subject Test: Math Resources

## Example Questions

### Example Question #1 : Vectors & Spaces

Calculate the dot product of the following vectors:

**Possible Answers:**

**Correct answer:**

Write the formula for dot product given and .

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

### Example Question #1 : Vector Form

Express in vector form.

**Possible Answers:**

**Correct answer:**

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

Express in vector form.

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

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 #5 : Vectors

Find the dot product of the 2 vectors.

**Possible Answers:**

**Correct answer:**

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

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.

**Possible Answers:**

**Correct answer:**

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

Compute: given the following vectors. and .

**Possible Answers:**

The answer does not exist.

**Correct answer:**

The answer does not exist.

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

What is the vector form of ?

**Possible Answers:**

**Correct answer:**

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

### Example Question #1 : Vector Form

Express in vector form.

**Possible Answers:**

**Correct answer:**

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 #10 : Vectors

Express in vector form.

**Possible Answers:**

**Correct answer:**

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

.

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