# ANSWERS to Ch. 11 Review Problems

11.1 #8 (a) see below (b) 5; √(26); <-3/5, 4/5>; <1/√(26), -5/√(26)> (c) -4/3; -5; 53°; 79° #18 <-√(3), 2> #22 <-1/√(2), 1/√(2)>; <1/√(2), -1/√(2)> #44 (a) <230, 40> (b) <170, -40> 11.2 #14 3; 5; 7.87; 4; 6.40; 7.48; none #18 (1,0,2); (5,0,5); (1,5,5); (5,5,2); (5,5,5); 60 #28 (x-1)2+(y-2)2+(z-3)2=16 #32 (3,2,0); 5 #40 cylinder of radius 2 centered around the y-axis #S10 (a) 0 (b) 10

11.3 #6 <14,10,16>; 5√(3); 6; 23.49; <2√(3)/5,√(3)/5,2√(3)/5>; <2/3,2/3,-1/3>; <0.596,0.426,0.681> #18 D; C #34 x(t) = -3t; y(t) = -2+3t; z(t) = 4-3t

11.4 #2 2; 2; 41; 43; -94 #8 86.67°; 117.9°; 62.1°; 71.8° #26 90° #30 <0,1,0> #58 <–8/21,16/21,–4/21>; <2/7, 4/7, 6/7>

11.5 #6 -1 #8 -42 #14 (a) <2,10,-8> (b) 0 (c) 0 (d) 2√(42) #20 not defined #34 18; 9 #36 see below; 18 #40 see below; 78  11.6 #2 x(t) = -3t, y(t) = 5+t, z(t) = -2-4t #6 x(t) = 7-2t, y(t) = 3-3t, z(t) = -4+2t #10 (6,-3,2); 45.8° #14 3x+y-5z = 14 #18 y=5 #24 2x+3y–z = 0 #36 x(t) = 4, y(t) = t, z(t) = 8+5t #54 22/√(38) #56 20/√(133) #58 intersect at (2,3,4)