# Calculus 3 : Dot Product

## Example Questions

### Example Question #121 : Dot Product

Find the dot product between  and

Explanation:

The formula for the dot product between two vectors  and  is . Using the vectors in the problem statement, this becomes .

### Example Question #122 : Dot Product

Solve:

Explanation:

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

Using this, we get

### Example Question #123 : Dot Product

Find the dot product between the vectors  and .

Explanation:

The formula for the dot product between two vectors  and  is . We then get

### Example Question #124 : Dot Product

Solve:

Explanation:

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

### Example Question #125 : Dot Product

Find the dot product between the vectors  and .

Explanation:

he formula for the dot product between two vectors  and  is . We then get

### Example Question #126 : Dot Product

Find the dot product between the vectors  and

Explanation:

The formula for the dot product between two vectors  and  is . Using the vectors from the problem statement, we get

### Example Question #127 : Dot Product

Solve:

Explanation:

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

### Example Question #128 : Dot Product

Find the dot product between  and

Explanation:

To find the dot product between two vectors  and  we use the formula . Using the vectors in the problem statement, we get

### Example Question #129 : Dot Product

Find the dot product between  and

Explanation:

To find the dot product between two vectors  and  we use the formula . Using the vectors in the problem statement, we get

### Example Question #130 : Dot Product

Find the dot product between  and