# Calculus 3 : Vectors and Vector Operations

## Example Questions

### Example Question #6 : Distance Between Vectors

Compute the distance between the vectors  and .

Explanation:

The formula for the distance between two vectors

and

is

.

Using the given vectors, we get

### Example Question #7 : Distance Between Vectors

Find the distance between the vectors  and .

Explanation:

To find the distance between the vectors, we use the formula

,

where one vector is

and the other is

.

Using the vectors we were given, we get

### Example Question #8 : Distance Between Vectors

Find the distance between the vectors  and .

Explanation:

To find the distance between the vectors, we use the formula

,

where one vector is

and the other is

.

Using the vectors we were given, we get

### Example Question #9 : Distance Between Vectors

The distance between (1, 3, -10) and (2, 5, 4) is

None of the Above

Explanation:

We use the distance formula:

### Example Question #10 : Distance Between Vectors

Given the points P:(2,1,5) andQ:(2,0,3). The magnitude of the vector from P to is:

None of the Above

Explanation:

First we need to find :

Therefore,

### Example Question #11 : Distance Between Vectors

Find the distance between the vectors  and .

Explanation:

To find the distance between two vectors  and  is . Using the vectors given, we get

### Example Question #12 : Distance Between Vectors

Find the distance between the vectors  and

Explanation:

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

### Example Question #13 : Distance Between Vectors

Find the distance between the vectors  and

Explanation:

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

### Example Question #14 : Distance Between Vectors

Find the distance between the vectors  and

Explanation:

To find the distance between two vectors  and , we use the formula . Plugging in the vectors from the problem statement, we get

### Example Question #15 : Distance Between Vectors

Find the distance between the vectors  and