# Calculus 3 : Vector Addition

## Example Questions

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### Example Question #71 : Vector Addition

Solve:

Explanation:

The sum of two vectors found by adding the corresponding components (for example, )

Our final answer is

(Note that the sum of two vectors produces another vector.)

### Example Question #72 : Vector Addition

Solve:

Explanation:

To add vectors, we add their corresponding components together (for example, )

Our final answer is

after using a Pythagorean identity to simplify.

### Example Question #73 : Vector Addition

Find the sum of the vectors  and

Explanation:

To find the sum of two vectors  and , you use the following formula:

Using the vectors from the problem statement, we get

### Example Question #74 : Vector Addition

Find the sum of the vectors  and

Explanation:

To find the sum of two vectors  and , you use the following formula:

Using the vectors from the problem statement, we get

### Example Question #75 : Vector Addition

Solve:

Explanation:

To add two vectors together, we simply add the corresponding components (for example, )

Our final answer is

### Example Question #76 : Vector Addition

Find the sum of the vectors  and

Explanation:

To find the sum of two vectors  and , we use the formula

Using the vectors from the problem statement, we get

### Example Question #77 : Vector Addition

Find the vector sum , where  and .

Explanation:

If  and , then the vector  , called the "sum" of two vectors, is defined by the sum of its respective components; that is,

.

We have  and . By the definition of the "sum" of two vectors, the vector  can be calculated as follows:

.

Hence, .

### Example Question #78 : Vector Addition

Find the sum of the vectors  and

Explanation:

To find the sum of two vectors  and , we use the formula

Using the vectors from the problem statement, we get

### Example Question #79 : Vector Addition

Find the sum of the vectors  and

Explanation:

To find the sum of two vectors  and , you use the formula

Using the vectors from the problem statement, we get

### Example Question #80 : Vector Addition

Find the sum of the vectors  and