Pre-Calc Homework Solutions 407

Pre-Calc Homework Solutions 407 - Section 10.2 3 2 407 26....

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Unformatted text preview: Section 10.2 3 2 407 26. x y 3 sin t, y 3 2 3 cos t; for t (x )2 (y )2 1 2 3 2 2 1 2 4 ,x , , and 1 3 1 3 3 3. , , 1 2 1 2 32. Since u and v are nonzero, we know that u 0 and v 0. Therefore, the dot product u v u v cos is 0 if and only if cos 0, which occurs if and only if u and v are . orthogonal 2 Tangent: Normal: , 2 3 , . 33. (r1, r2) v u (u1, u2) u+v u v 3 2 , 27. AB E BA E AB E AC E 3, 1 , BC E 3, BA E CA E 1 , CB E 1, 3 , and AC E 2, 2. (v1, v2) 1, 3 , and CA E CB E 2, 2 . 10, and 10, BC E 2 2. cos cos cos 1 Angle at A AB AC E E AB AC E E 3(2) 1( 2) ( 1 5 10)(2 2) r1 r2 v1 v2 u1 so r1 u2 so r2 u1 u2 v1 v2 1 34. (a) To find u v, place both vectors with their initial points at the origin. The vector drawn from the terminal point of v to the terminal point of u is u v. Or, add u and v according to the parallelogram law. (b) 1 63.435 , Angle at B BC E E BA cos 1 BC BA E E (u1, u2) cos cos Angle at C 1 ( 1)( 3) ( 10)( ( 3)( 1) 10) v uv u uv v (r1, r2) 1 3 5 53.130 , and CB CA E E cos 1 CB CA E E v (v1, v2) u cos cos 28. AC E 1 1( 2) ( 3(2) 10)(2 2) 1 5 1 63.435 . 2. 0, so the angle measures 90 . w2) r1 r2 ( v1) ( v2) u1 r1 u2 r2 u1 u2 v1 v2 2, 4 and BD E 2(4) 4, 35. (a) Let P 1 OP E 2 (a (a, b) and Q 1 OQ E 2 c) (b d) , 2 2 2 OP E 3 1 OP E 3 (c, d). Then 1 a, b 2 1 c, d 2 AC BD E E 4( 2) 29. (a) u (v w) u1(v1 w1) u2(v2 (u1v1 u1w1) (u2v2 u2w2) (u1v1 u2v2) (u1w1 u2w2) u v u w (b) (u OM E v) w (u1 v1)w1 (u2 v2)w2 (u1w1 v1w1) (u2w2 v2w2) (u1w1 u2w2) (v1w1 v2w2) u w v w u12 u2 2 v) v1) u22 (v12 (u2 v22 v22) v2)(u2 v2) ( u12 u22)2 u2 (b) OM E (c) OM E 1 OQ E 3 2 OQ E 3 30. u u 31. (u u1 u v) (u (u1 2 v1)(u1 v1 2 (u12 2 u22) v2 ...
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