Calculus 3 : Vector Addition

Study concepts, example questions & explanations for Calculus 3

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Example Questions

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Example Question #71 : Vector Addition

Solve:

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

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 

Possible Answers:

Correct answer:

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 #281 : Vectors And Vector Operations

Find the sum of the vectors  and 

Possible Answers:

Correct answer:

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 #282 : Vectors And Vector Operations

Solve:

Possible Answers:

Correct answer:

Explanation:

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

Our final answer is

 

Example Question #283 : Vectors And Vector Operations

Find the sum of the vectors  and 

Possible Answers:

Correct answer:

Explanation:

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

 

Using the vectors from the problem statement, we get

Example Question #284 : Vectors And Vector Operations

Find the vector sum , where  and .

Possible Answers:

Correct answer:

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 #285 : Vectors And Vector Operations

Find the sum of the vectors  and 

Possible Answers:

Correct answer:

Explanation:

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

 

Using the vectors from the problem statement, we get

 
 

 

Example Question #286 : Vectors And Vector Operations

Find the sum of the vectors  and 

Possible Answers:

Correct answer:

Explanation:

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

Using the vectors from the problem statement, we get

Example Question #287 : Vectors And Vector Operations

Find the sum of the vectors  and 

Possible Answers:

Correct answer:

Explanation:

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

Using the vectors from the problem statement, we get

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