Calculus 3 : Calculus 3

Study concepts, example questions & explanations for Calculus 3

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Example Questions

Example Question #2331 : Calculus 3

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 #2332 : Calculus 3

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 #331 : Vectors And Vector Operations

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 #2334 : Calculus 3

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 #18 : 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 #19 : 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 #13 : 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 #332 : Vectors And Vector Operations

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 #333 : Vectors And Vector Operations

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 #334 : Vectors And Vector Operations

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 the dot product is zero, these two vectors are perpendicular!

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