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# Problem: You are given two vectors: A = −3.00 î + 5.00 ĵ and B = 8.00 î + 2.00 ĵ. Let the counterclockwise angles be positive. Vector C is the sum of A and B , so C = A + B. What angle θC, where 0° ≤ θC &lt; 360°, does C make with the +x-axis?

###### FREE Expert Solution

Vector direction:

$\overline{){\mathbf{tan}}{\mathbf{\theta }}{\mathbf{=}}\frac{\mathbf{y}}{\mathbf{x}}}$

C = A + B = (-3 + 8) + (5 + 2) = 5  + 7

θC = tan-1 (7/5) = 54.5°

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###### Problem Details

You are given two vectors: A = −3.00 î + 5.00 and B = 8.00 î + 2.00 . Let the counterclockwise angles be positive.

Vector C is the sum of A and B , so C = A + B. What angle θC, where 0° ≤ θC < 360°, does C make with the +x-axis?