# Calculus 3 : Dot Product

## Example Questions

### Example Question #416 : Vectors And Vector Operations

Solve:

Explanation:

The dot product of two vectors is given by

Using this, we get

### Example Question #417 : Vectors And Vector Operations

Solve:

Explanation:

The dot product of two vectors is given by

Using this, we get

### Example Question #418 : Vectors And Vector Operations

Solve:

Explanation:

The dot product of two vectors is given by

### Example Question #419 : Vectors And Vector Operations

Find the dot product of the vectors  and

Explanation:

The formula for the dot product is . Using the given vectors, we get .

### Example Question #420 : Vectors And Vector Operations

Compute the dot product between  and .

Explanation:

The formula for the dot product is . Using the two given vectors and solving, .

### Example Question #101 : Dot Product

Solve:

Explanation:

The dot product of two vectors is given by

### Example Question #102 : Dot Product

Solve:

Explanation:

The dot product of two vectors is found by adding the product of the corresponding components. (For example, .)

For our vectors, we get

### Example Question #103 : Dot Product

Solve:

Explanation:

The dot product of two vectors is given by the sum of the products of the corresponding components (for example, ).

So, we get

### Example Question #104 : Dot Product

Solve:

Explanation:

The dot product of two vectors is given by

So, we get

We used a Pythagorean trigonometric identity to simplify.

Solve: