Calculus 3 : Dot Product

Study concepts, example questions & explanations for Calculus 3

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Example Questions

Example Question #111 : Dot Product

Solve:

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 answer is

Example Question #427 : Vectors And Vector Operations

Find 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 #112 : Dot Product

Find 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 #427 : Vectors And Vector Operations

Compute , where  and .

Possible Answers:

Correct answer:

Explanation:

The formula for the dot product is 

.

Using the given vectors, we get 

.

Example Question #2432 : Calculus 3

Compute the dot product of the vectors  and .

Possible Answers:

Correct answer:

Explanation:

The formula for the dot product of vectors 

 

and 

 

is 

.

Using the vectors we were given, this becomes 

 which equals 

Example Question #2433 : Calculus 3

Let a = (1,2,1), b = (2,3,2), and c = (2,0,4). Then 

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

Lets start by :

Then we multiply :

Example Question #112 : Dot Product

Find all numbers x for which 2i+5j+2xk ⊥ 6i+4jxk:

Possible Answers:

Correct answer:

Explanation:

if 2i+5j+2x⊥ 6i+4jxk, then the dot product of the two vectors should be 0.

Therefore,

 

Example Question #2434 : Calculus 3

Find the dot product between 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 #431 : Vectors And Vector Operations

Find the dot product between  and 

Possible Answers:

Correct answer:

Explanation:

The formula for the dot product between two vectors  and  is . Using the vectors in the problem statement, this becomes .

Example Question #432 : Vectors And Vector Operations

Evaluate 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

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