# Calculus 3 : Dot Product

## Example Questions

### Example Question #141 : Dot Product

Find the dot product between the vectors  and

Explanation:

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

. Applying to the vectors from the problem statement, we get:

### Example Question #142 : Dot Product

Find the dot product between the vectors  and

Explanation:

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

. Applying to the vectors from the problem statement, we get:

### Example Question #143 : Dot Product

Find the dot product of the two vectors:

Explanation:

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

### Example Question #144 : Dot Product

What is the product of  and

Explanation:

### Example Question #145 : Dot Product

Evaluate the dot product of the vectors .

Explanation:

To evaluate the dot product of any two vectors, we multiply them component-wise.

.

### Example Question #146 : Dot Product

Solve:

Explanation:

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

### Example Question #147 : Dot Product

Evaluate the dot product of the two vectors.

Explanation:

The dot product for the vectors

is defined as

For the vectors in this problem we find that

### Example Question #148 : Dot Product

Evaluate the dot product of the two vectors

Explanation:

The dot product for the vectors

is defined as

For the vectors in this problem we find that

### Example Question #149 : 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, we get

### Example Question #150 : Dot Product

Find the dot product between the vectors  and