GRE Subject Test: Math : Vectors

Study concepts, example questions & explanations for GRE Subject Test: Math

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Example Questions

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Example Question #1 : Vectors

Calculate the dot product of the following vectors:  

 

Possible Answers:

Correct answer:

Explanation:

Write the formula for dot product given  and .

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

Example Question #1 : Vector

Express  in vector form.

Possible Answers:

Correct answer:

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 #2 : Vectors

Express  in vector form.

Possible Answers:

Correct answer:

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 .

Possible Answers:

Correct answer:

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 #3 : Vector

Find the dot product of the 2 vectors.  

Possible Answers:

Correct answer:

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 #4 : Vector

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:

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 #5 : Vector

Compute:   given the following vectors.   and .

Possible Answers:

The answer does not exist.

Correct answer:

The answer does not exist.

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 #6 : Vector

What is the vector form of ?

Possible Answers:

Correct answer:

Explanation:

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

Example Question #7 : Vector

Express  in vector form.

Possible Answers:

Correct answer:

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 #8 : Vector

Express  in vector form.

Possible Answers:

Correct answer:

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 

.

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