Calculus 3 : Dot Product

Study concepts, example questions & explanations for Calculus 3

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Example Questions

Example Question #91 : Dot Product

Find the length  of the vector .

Possible Answers:

Correct answer:

Explanation:

To find the length  of the vector , we take the square root of the dot product :

Example Question #92 : Dot Product

Find the length  of the vector .

Possible Answers:

Correct answer:

Explanation:

To find the length  of the vector , we take the square root of the dot product :

Example Question #93 : Dot Product

Find the length  of the vector .

Possible Answers:

Correct answer:

Explanation:

To find the length  of the vector , we take the square root of the dot product :

Example Question #94 : Dot Product

Find 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 #95 : Dot Product

Find 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 #411 : Vectors And Vector Operations

Calculate the dot product

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 #412 : Vectors And Vector Operations

Find the vector projection of  onto .

Possible Answers:

None of the other answers

Correct answer:

Explanation:

To find the vector projection of  onto , we take the scalar projection , and multiply it to a vector of unit length; .

Hence for the vector projection of  onto , we have

     

  .

Example Question #413 : Vectors And Vector Operations

Find the vector projection of  onto .

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

To find the vector projection of  onto , we take the scalar projection , and multiply it to a vector of unit length; .

Hence for the vector projection of  onto , we have

     

  .

Example Question #414 : Vectors And Vector Operations

Find the dot product of  and 

Possible Answers:

Correct answer:

Explanation:

 

Example Question #415 : Vectors And Vector Operations

Simplify:

Possible Answers:

Correct answer:

Explanation:

The dot product of two vectors is given by:

Using this, for our vectors, we get

 

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