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Find the sum of the vectors <7,−2> and <1,8>. Then find the magnitude and direction of the resultant vector. Round angles to the nearest degree and other values to the nearest tenth.

Find the sum of the vectors <7,−2> and <1,8>. Then find the magnitude-example-1
User Tenatious
by
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1 Answer

2 votes

Answer:

The sum of the vectors is <8 , 6>

The magnitude of the resultant vector is 10

The direction of the resultant vector is 37°

The answer is the 1st answer: <8 , 6> ; 10 ; 37°

Explanation:

* Lets explain how to solve the problem

∵ The first vector is <7 , -2>

∵ The second vector is <1 , 8>

∴ The sum of the 2 vectors = <7 , -2> + <1 , 8>

∴ Their sum = <7 + 1 , -2 + 8> = <8 , 6>

* The sum of the vectors is <8 , 6>

- The magnitude of the resultant vector = √(x² + y²)

∵ x = 8 and y = 6

∴ The magnitude of the resultant vector = √(8² + ²)

∴ The magnitude of the resultant vector = √(36 + 64) = √100 = 10

* The magnitude of the resultant vector is 10

- The direction of the vector = tan^-1 (y/x)

∵ x = 8 and y = 6

∴ The direction of the vector = tan^-1 (6/8) = 36.869 ≅ 37°

* The direction of the resultant vector is 37°

User Romedius
by
6.2k points
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