Calculus 3 : Dot Product

Study concepts, example questions & explanations for Calculus 3

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Example Questions

Example Question #141 : Dot Product

Find the dot product between the vectors  and 

Possible Answers:

Correct answer:

Explanation:

To find the dot product between vectors  and , you apply the following formula:

. Applying to the vectors from the problem statement, we get:

Example Question #142 : Dot Product

Find the dot product between the vectors  and 

Possible Answers:

Correct answer:

Explanation:

To find the dot product between vectors  and , you apply the following formula:

. Applying to the vectors from the problem statement, we get:

Example Question #143 : Dot Product

Find the dot product of the two vectors:

Possible Answers:

Correct answer:

Explanation:

The dot product of two vectors is given by the sum of the products of the corresponding components (for example, )

Our final answer is

Example Question #144 : Dot Product

What is the product of  and 

Possible Answers:

Correct answer:

Explanation:

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Example Question #145 : Dot Product

Evaluate the dot product of the vectors .

Possible Answers:

None of the other answers

Correct answer:

Explanation:

To evaluate the dot product of any two vectors, we multiply them component-wise.

 

.

Example Question #146 : Dot Product

Solve:

Possible Answers:

Correct answer:

Explanation:

The dot product of two vectors is given by the sum of the products of their respective components (for example, )

Our final answer is

Example Question #147 : Dot Product

Evaluate the dot product of the two vectors.

Possible Answers:

Correct answer:

Explanation:

The dot product for the vectors

is defined as

For the vectors in this problem we find that

Example Question #148 : Dot Product

Evaluate the dot product of the two vectors

Possible Answers:

Correct answer:

Explanation:

The dot product for the vectors

is defined as

For the vectors in this problem we find that

Example Question #149 : Dot Product

Find the dot product between the vectors  and 

Possible Answers:

Correct answer:

Explanation:

To find the dot product between two vectors  and , we use the formula 

Using the vectors from the problem statement, we get

Example Question #150 : Dot Product

Find the dot product between the vectors  and 

Possible Answers:

Correct answer:

Explanation:

To find the dot product between two vectors  and , we use the formula 

Using the vectors from the problem statement, we get

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