Calculus 3 : Dot Product

Example Questions

Example Question #51 : Dot Product

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

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:

Since the dot product is zero, it can be inferred that these two vectors are perpendicular!

Example Question #52 : Dot Product

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

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 #53 : Dot Product

Find the dot product between the two vectors and

Explanation:

To take the dot product of two vectors, we multiply their common components, and then add.

.

Example Question #54 : Dot Product

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

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 #55 : Dot Product

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

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 #56 : Dot Product

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

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 #57 : Dot Product

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

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 #58 : Dot Product

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

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 #59 : Dot Product

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

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 #60 : Dot Product

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