20.1 a) CrossProduct[(1,0,0),(1,-5,-2)] -(0,2,-5).(3,-1,1) b) CrossProduct[(0,1,0),(4,1,-3)] -(-3,0,-4).(3,4,0) c) CrossProduct[(0,0,1),(2,5,7)] -(-5,2,0).(1,3,4) 20.2 a) CrossProduct[(1,4,0),(3,-2,1)] -(4, -1, -14).(0,0,0) b) CrossProduct[(2,1,1),(-4,-3,-1)] -(2, -2, -2).(-1,7,-6) c) CrossProduct[(1,0,-3),(-1,1,0)] -(3, 3, 1).(3,-1,2) 20.3 a) -(2, 3, -5).(0,0,6) b) -(-1, 4, 7).(0,3,0) 20.4 LinearSolve[{{5,0,-1},{2,-1,-4},{0,3,2},{3,4,5}},{-3,-5,1,3}] 20.5 -(1, -2, 3).(1,-2,1) 20.7 a) arccos(|(-2,4,-1).(7,3,-2)|/sqrt(((-2,4,-1).(-2,4,-1))*((7,3,-2).(7,3,-2)))) b) arccos(|(0,1,0).(0,3,-3)|/sqrt(((0,1,0).(0,1,0))*((0,3,-3).(0,3,-3)))) 20.8 CrossProduct[(3,-2,1),(1,0,-2)] CrossProduct[(4,7,2),(1,-2,1)] -(11,-2,-15).(2,2,1) 20.10 a) |(1,2,1).(1,2,2)-10|/sqrt((1,2,2).(1,2,2)) b) |(0,0,0).(15,-10,6)-190|/sqrt((15,-10,6).(15,-10,6)) c) |(2,8,5).(1,-2,-2)-1|/sqrt((1,-2,-2).(1,-2,-2)) 20.13 :( 20.14 a),b),d) :-( 20.15 CrossProduct[(3,7,-2),(2,-6,7)] 20.16 CrossProduct[(2,-3,4),(0,1,0)] 20.17 a) arcsin(|(4,3,1).(3,5,-1)|/sqrt(((4,3,1).(4,3,1))*((3,5,-1).(3,5,-1)))) b) arcsin(|(2,4,3).(3,-3,2)|/sqrt(((2,4,3).(2,4,3))*((3,-3,2).(3,-3,2)))) c) CrossProduct[(3,5,-7),(2,-1,1)] arcsin(|(-2, -17, -13).(5,0,-1)|/sqrt(((-2, -17, -13).(-2, -17, -13))*((5,0,-1).(5,0,-1)))) LinearSolve[{{3,5,-7},{2,-1,1},{5,0,-1}},{-16,6,4}]