# Calculus 3 : Dot Product

## Example Questions

### Example Question #161 : Dot Product

Find the dot product between the vectors  and

Explanation:

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

Using the vectors from the problem statement, we get

### Example Question #162 : 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 #163 : 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 #164 : 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 and applying, we get

### Example Question #165 : 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 and applying, we get

### Example Question #166 : 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 and applying, we get

### Example Question #167 : Dot Product

Find the dot product between the vectors  and

Explanation:

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

Using the vectors from the problem statement, we get

### Example Question #168 : Dot Product

Find the dot product between the vectors  and

Explanation:

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

Using the vectors from the problem statement, we get

### Example Question #169 : Dot Product

Solve:

Explanation:

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

Solve for x: