# Calculus 3 : Dot Product

## Example Questions

### Example Question #81 : Dot Product

Find the dot product:

Explanation:

Write the dot product formula.

Substitute the values of the vectors and solve.  The dot product will result in a number, not a vector.

The dot product is:

### Example Question #82 : Dot Product

Find the length  of the vector

Explanation:

To find the length  of the vector , we take the square root of the dot product :

### Example Question #83 : Dot Product

Find the length  of the vector .

Explanation:

To find the length  of the vector , we take the square root of the dot product :

### Example Question #84 : Dot Product

Find the length  of the vector .

Explanation:

To find the length  of the vector , we take the square root of the dot product :

### Example Question #85 : Dot Product

Find the length  of the vector .

Explanation:

To find the length  of the vector , we take the square root of the dot product :

### Example Question #86 : Dot Product

Find the length  of the vector .

Explanation:

To find the length  of the vector , we take the square root of the dot product :

### Example Question #87 : Dot Product

Find the length  of the vector .

Explanation:

To find the length  of the vector , we take the square root of the dot product :

### Example Question #88 : Dot Product

Find the length  of the vector .

Explanation:

To find the length  of the vector , we take the square root of the dot product :

### Example Question #89 : Dot Product

Find the length  of the vector .

Explanation:

To find the length  of the vector , we take the square root of the dot product :

### Example Question #90 : Dot Product

Find the length  of the vector .