### All Calculus 3 Resources

## Example Questions

### Example Question #1 : Distance Between Vectors

Given the vectors

find the distance between them, .

**Possible Answers:**

**Correct answer:**

To find the distance between the vectors

we do the following calculation:

### Example Question #2 : Distance Between Vectors

Find the distance between the two vectors

**Possible Answers:**

**Correct answer:**

To find the distance between the two vectors

we make the following calculation

### Example Question #3 : Distance Between Vectors

Find the Euclidian distance between the two vectors:

**Possible Answers:**

**Correct answer:**

The Euclidian distance between two vectors is:

Plugging in the numbers given, we have:

### Example Question #4 : Distance Between Vectors

Find the distance between if and .

**Possible Answers:**

**Correct answer:**

Write the formula to find the magnitude of the vector .

Substitute the points into the equation assuming and .

The answer is:

### Example Question #5 : Distance Between Vectors

Calculate the length of line segment *AB *given *A*(−5, −2, 0) and *B*(6, 0, 3):

**Possible Answers:**

None of the Above

**Correct answer:**

First we need to find

so

### Example Question #6 : Distance Between Vectors

Compute the distance between the vectors and .

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

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

**Possible Answers:**

None of the Above

**Correct answer:**

We use the distance formula:

### Example Question #10 : Distance Between Vectors

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

**Possible Answers:**

None of the Above

**Correct answer:**

First we need to find :

Therefore,