Question

2.24 Given vectors A = 2a, + 4a, + 10a, and B =-5a, + аф-3a, find (a) A + B at P(0, 2,-5) (b) The angle between A and B at P (c) The scalar component of A along B at P

Answer 1

Consider the vectors A bar = 2a hat x + 4 x hat y + 10a hat z B bar = -5a hat e + a hat_phi + 3 hat z Convert vector B bar into correction coordinates [Bx By Bz] = [cos phi sin phi 0 -sin phi cos phi 0 0 0 1] [Bx B phi B z] = [cos phi sin phi 0 -sin phi cos phi 0 0 0 1] [-5 1 -3] = [-5 cos phi - sin phi -5 sin phi + cos phi 0 + 0 - 3] [Bx By Bz] = [-5 cos phi - sin phi -5 sin phi + cos phi -3] Therefore A bar + B bar = (2a hat x + 4a hat y + 10a hat z) + (-5 cos phi - sin phi) b hat x (-5 sin phi + cos phi) a hat y - 3 a hat z p(0, 2, -5) rightwardsdoublearrow phi = tan^-1 (y/x) = tan^-1 (2/0)phi = 90 degree = 2 hat x + 4a hat y + 10z hat + (-5 cos 90 degree - sin 90 degree) a hat x + (-5 sin 90 degree + cos 90 degree) a hat y - 3a hat z)