Question # 1: find A . B, where A = (5, 30 o ) and B =(3,90 o ). Question # 2: f

Question

Question # 1:
find A . B, where A = (5, 30o) and B =(3,90o). Question # 2: find A . B, where A = 3i - 4j and B = -5i - 12j Question # 3: find the angle between   A = 3i - 4j and B = -5i-12j Question # 4: find the component of A - 3i - 4j that is parallel to B = -5i-12j Question # 5: show that r^ = cosi^ + sinj^ is perpendicular to t^ = -sini + cosj. Question # 1:
find A . B, where A = (5, 30o) and B =(3,90o). Question # 2: find A . B, where A = 3i - 4j and B = -5i - 12j Question # 3: find the angle between   A = 3i - 4j and B = -5i-12j Question # 4: find the component of A - 3i - 4j that is parallel to B = -5i-12j Question # 5: show that r^ = cosi^ + sinj^ is perpendicular to t^ = -sini + cosj.

Explanation / Answer

( 1 ) . A.B = 5* 3 * cos ( 90 -30 )                 = 7.5 (2). A.B = ( 3 * -5 ) + ( -4 * -12 )               =-15 + 48 = 33 (3). Let the angle be then cos = A.B/ [ mod A * mod B ]                                                     = 33 / [ [3 ^ 2 + 4 ^ 2 ] * [ 5 ^ 2 + 12 ^ 2]]                                                     = 33 / ( 5 * 13 )                                                   =59.48 degrees

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