Calculus 3 : Dot Product

Study concepts, example questions & explanations for Calculus 3

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Example Questions

Example Question #71 : Dot Product

Given the following two vectors,  and , calculate the dot product between them,.

Possible Answers:

Correct answer:

Explanation:

The dot product of a paired set of vectors can be found by summing up the individual products of the multiplications between matched directional vectors.

Note that the dot product is a scalar value rather than a vector; there's no directional term.

Now considering our problem, we're given the vectors

 and 

The dot product can be found following the example above:

Example Question #72 : Dot Product

Given the following two vectors,  and , calculate the dot product between them,.

Possible Answers:

Correct answer:

Explanation:

The dot product of a paired set of vectors can be found by summing up the individual products of the multiplications between matched directional vectors.

Note that the dot product is a scalar value rather than a vector; there's no directional term.

Now considering our problem, we're given the vectors

 and 

The dot product can be found following the example above:

Example Question #73 : Dot Product

Given the following two vectors,  and , calculate the dot product between them,.

Possible Answers:

Correct answer:

Explanation:

The dot product of a paired set of vectors can be found by summing up the individual products of the multiplications between matched directional vectors.

Note that the dot product is a scalar value rather than a vector; there's no directional term.

Now considering our problem, we're given the vectors

 and 

The dot product can be found following the example above:

Example Question #74 : Dot Product

Given the following two vectors,  and , calculate the dot product between them,.

Possible Answers:

Correct answer:

Explanation:

The dot product of a paired set of vectors can be found by summing up the individual products of the multiplications between matched directional vectors.

Note that the dot product is a scalar value rather than a vector; there's no directional term.

Now considering our problem, we're given the vectors

 and 

The dot product can be found following the example above:

Example Question #75 : Dot Product

Given the following two vectors,  and , calculate the dot product between them,.

Possible Answers:

Correct answer:

Explanation:

The dot product of a paired set of vectors can be found by summing up the individual products of the multiplications between matched directional vectors.

Note that the dot product is a scalar value rather than a vector; there's no directional term.

Now considering our problem, we're given the vectors

 and 

The dot product can be found following the example above:

Example Question #76 : Dot Product

Given the following two vectors,  and , calculate the dot product between them,.

Possible Answers:

Correct answer:

Explanation:

The dot product of a paired set of vectors can be found by summing up the individual products of the multiplications between matched directional vectors.

Note that the dot product is a scalar value rather than a vector; there's no directional term.

Now considering our problem, we're given the vectors

 and 

The dot product can be found following the example above:

Example Question #77 : Dot Product

Given the following two vectors,  and , calculate the dot product between them,.

Possible Answers:

Correct answer:

Explanation:

The dot product of a paired set of vectors can be found by summing up the individual products of the multiplications between matched directional vectors.

Note that the dot product is a scalar value rather than a vector; there's no directional term.

Now considering our problem, we're given the vectors

 and 

The dot product can be found following the example above:

Example Question #78 : Dot Product

Evaluate the dot product .

Possible Answers:

None of the other answers

Correct answer:

None of the other answers

Explanation:

The correct answer is .

 

To compute the dot product, we take the corresponding components of each vector, and multiply them together. In this case, we have .

Note that taking the dot product of any two vectors will always return a scalar-valued expression (or just a simple scalar). There should be no vector brackets in your answer.

Example Question #79 : Dot Product

Find the dot product of the two vectors:

Possible Answers:

20.72

19.07

23.58

22.14

25.32

Correct answer:

25.32

Explanation:

The dot product of two vectors is defined as:

For the given vectors, this is:

Example Question #80 : Dot Product

Find the magnitude of the following vector:

Possible Answers:

Correct answer:

Explanation:

The magnitude of a vector is given by:

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