Two vectors, A with magnitude 18.0 units is directed at an angle of 26.0 deg bel

Question

Two vectors, A with magnitude 18.0 units is directed at an angle of 26.0 deg below the +x-axis and B is 16.0 units long directed at an angle of 21.0 deg to the right of the +y-axis. Find the angle of the vector A - B measured relative to the positive x-axis.

Explanation / Answer

Decompose: x dir: A = 18 cos 26, B = 16 sin 21 (rel. to y given so sin) => A - B = 18 cos 26 - 16 sin 21 = 10.444 y dir: A = - 18 sin 26, B = 16 cos 21 (rel. to y given so cos) => A - B = - 18 sin 26 - 16 cos 21 = -22.828 angle = tan^-1 (y/x) = 65.42 degrees y -ve, x +ve so angle = -65.42 degrees = 360 - 65.42 degrees (4th quadrant)

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