Calculus 3 : Vectors and Vector Operations

Study concepts, example questions & explanations for Calculus 3

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Example Questions

Example Question #371 : 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 #372 : 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 #373 : 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 #374 : 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 #375 : 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 #376 : 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 #2376 : 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 #2377 : 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 #377 : 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 #378 : 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:

Observe from this zero result that the two vectors must be perpendicular!

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