Calculus 3 : Dot Product

Study concepts, example questions & explanations for Calculus 3

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Example Questions

Example Question #31 : 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 #32 : 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 #33 : 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:

Note that if you were to find the magnitude of each vector and multiply the two, you'd find the result. This is because these two vectors happen to be parallel.

Example Question #34 : 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:

The zero result shows that these two vectors are perpendicular.

Example Question #35 : 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:

Note that since we found a zero value, these two vectors must be perpendicular!

Example Question #36 : 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 #37 : 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 #38 : Dot Product

Find the dot product between the two vectors. 

Possible Answers:

Correct answer:

Explanation:

The dot product for two vectors  and 

is defined as 

Fo the given vectors 

Example Question #39 : Dot Product

Find the dot product of the two vectors. 

Possible Answers:

Correct answer:

Explanation:

The dot product for two vectors  and 

is defined as 

Fo the given vectors 

Example Question #40 : Dot Product

Find the dot product  of the two vectors

Possible Answers:

Correct answer:

Explanation:

To find the dot product , we calculate

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