Calculus 3 : Vectors and Vector Operations

Study concepts, example questions & explanations for Calculus 3

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Example Questions

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 #8 : 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,

Example Question #11 : Distance Between Vectors

Find the distance between the vectors  and .

Possible Answers:

Correct answer:

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 

Possible Answers:

Correct answer:

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 

Possible Answers:

Correct answer:

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 

Possible Answers:

Correct answer:

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 

Possible Answers:

Correct answer:

Explanation:

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

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