# Calculus 3 : Dot Product

## Example Questions

### Example Question #71 : 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 #72 : 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 #73 : 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 #74 : 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 #75 : 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 #76 : 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 #77 : 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 #78 : Dot Product

Evaluate the dot product .

Explanation:

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:

20.72

19.07

23.58

22.14

25.32

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: