Calculus 3 : Dot Product

Study concepts, example questions & explanations for Calculus 3

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Example Questions

Example Question #161 : 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 apply the formula

Using the vectors from the problem statement, we get

Example Question #162 : 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 apply the following formula:

Using the vectors from the problem statement, we get

Example Question #163 : 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 apply the following formula:

Using the vectors from the problem statement, we get

Example Question #164 : Dot Product

Find the dot product between the vectors  and 

Possible Answers:

Correct answer:

Explanation:

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

Using the vectors from the problem statement and applying, we get

Example Question #165 : Dot Product

Find the dot product between the vectors  and 

Possible Answers:

Correct answer:

Explanation:

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

Using the vectors from the problem statement and applying, we get

Example Question #166 : Dot Product

Find the dot product between the vectors  and 

Possible Answers:

Correct answer:

Explanation:

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

Using the vectors from the problem statement and applying, we get

Example Question #167 : Dot Product

Find the dot product between the vectors  and 

Possible Answers:

Correct answer:

Explanation:

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

Using the vectors from the problem statement, we get

Example Question #168 : Dot Product

Find the dot product between the vectors  and 

Possible Answers:

Correct answer:

Explanation:

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

Using the vectors from the problem statement, we get

Example Question #169 : Dot Product

Solve:

 

Possible Answers:

Correct answer:

Explanation:

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

Our final answer is

Example Question #170 : Dot Product

Solve for x:

Possible Answers:

Correct answer:

Explanation:

To solve for x, we must take the dot product, which is performed by multiplying the corresponding components and adding the products together.

We get

Solving for x, we get

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