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.

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 <8 , 6> ; 10 ; 37°

Step-by-step 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°

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