# Calculus 3 : Distance between Vectors

## Example Questions

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### Example Question #1 : Distance Between Vectors

Given the vectors

find the distance between them, .

Possible Answers:

Correct answer:

Explanation:

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:

Explanation:

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:

Explanation:

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:

Explanation:

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:

Explanation:

First we need to find

so

### Example Question #6 : Distance Between Vectors

Compute the distance between the vectors  and .

Possible Answers:

Correct answer:

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 .

Possible Answers:

Correct answer:

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 #1 : Distance Between Vectors

Find the distance between the vectors  and .

Possible Answers:

Correct answer:

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

Possible Answers:

None of the Above

Correct answer:

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:

Possible Answers:

None of the Above

Correct answer:

Explanation:

First we need to find :

Therefore,

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