# Calculus 3 : Dot Product

## Example Questions

### Example Question #151 : Dot Product

Find the dot product between the vectors  and

Explanation:

To find the dot product between the vectors  and , we use the formula

Using the vectors from the problem statement, we then get

### Example Question #152 : Dot Product

Find the dot product between the vectors  and

Explanation:

To find the dot product between the vectors  and , we use the formula

Using the vectors from the problem statement, we then get

### Example Question #153 : Dot Product

Find the dot product between the vectors  and

Explanation:

To find the dot product between two vectors  and , we use the formula:

Using the vectors from the problem statement and applying, we get

### Example Question #154 : Dot Product

Find the dot product between the vectors  and

Explanation:

To find the dot product between two vectors  and , we use the formula:

Using the vectors from the problem statement and applying, we get

### Example Question #155 : Dot Product

Find the dot product of the two vectors.

Explanation:

The dot product of two vectors

is defined as

For the vectors in this problem we have

### Example Question #156 : Dot Product

Find the dot product of the two vectors.

Explanation:

The dot product of two vectors

is defined as

For the vectors in this problem we have

### Example Question #157 : Dot Product

Find the dot product of the two vectors.

Explanation:

The dot product of two vectors

is defined as

For the vectors in this problem we have

### Example Question #158 : Dot Product

Find the dot product between the vectors  and

Explanation:

To find the dot product between two vectors  and , we apply the following formula:

Using the vectors from the problem statement, we get

### Example Question #159 : Dot Product

Find the dot product between the vectors  and

Explanation:

To find the dot product between two vectors  and , we apply the following formula:

Using the vectors from the problem statement, we get

### Example Question #160 : Dot Product

Find the dot product between the vectors  and