(a) Given the vectors A and B shown in Fig. 3-32 below ( A = 55.0 and = 55.5 °),
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Question
(a) Given the vectors A and B shown in Fig. 3-32 below (A = 55.0 and = 55.5°), determine B - A.
(b) Determine A - B without using your answer in (a).
(Compare your results and see if they are opposite.)
Magnitude Direction ° (counterclockwise from the +x axis is positive) igure 3-32 (a) Given the vectors A and B shown in Fig. 3-32 below (A = 55.0 and theta = 55.5 degree), determine B - A. Magnitude Direction degree (counterclockwise from the +x axis is positive) (b) Determine A - B without using your answer in (a). Magnitude Direction degree (counterclockwise from the +x axis is positive) (Compare your results and see if they are opposite.)Explanation / Answer
Vector A = 55 cos 28 i + 55 sin 28 j = 48.56 i + 25.82 j Vector B = 40 cos 55.5 (-i) + 40 sin 55.5 j = -22.656 i + 32.96 j B-A = -22.656 i + 32.96 j -48.56 i - 25.82 j = -71.216 i +7.145 j Magnitude of B-A = [ (-71.216) 2 +( 7.145) 2 ] = 71.57 Let B -A makes an angle with negative x axis along positive y axis then tan = 7.145 / 71.216 = 5.729 o Angle with positive x axis = 180 - = 174.27 o (b).A-B = -(B-A) = -[ -22.656 i + 32.96 j -48.56 i - 25.82 j ] = 71.216 i -7.145 j Magnitude of A-B = [ (71.216) 2 + (-7.145) 2 ] = 71.57 Let A-B makes an angle with positive x axis along negative y axis then tan = 7.145 / 71.216 = 5.729 o Angle with positive x axis along counter clockwise direction = 360 - = 354.27 o = -[ -22.656 i + 32.96 j -48.56 i - 25.82 j ] = 71.216 i -7.145 j Magnitude of A-B = [ (71.216) 2 + (-7.145) 2 ] = 71.57 Let A-B makes an angle with positive x axis along negative y axis then tan = 7.145 / 71.216 = 5.729 o Angle with positive x axis along counter clockwise direction = 360 - = 354.27 oRelated Questions
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