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Unformatted text preview: 1, b j k, b i
■ ■ ■ 0, 1, 2 ,
i j ■ c 4, k, c ■ ■ 2, 5
i ■ j ■ k
■ ■ ■ 31–32  Find the volume of the parallelepiped with adjacent edges
PQ, PR, and PS. 31. P 2, 0, 1, 32. P 0, 1, 2 ,
■ ■ Q 4, 1, 0 ,
Q 2, 4, 5 , ■ ■ R 3,
R ■ 1, 1 , 1, 0, 1 , ■ ■ S 2,
S 6, ■ 2, 2
1, 4 ■ ■ ■ ■ 33. Use the scalar triple product to verify that the vectors a 2i 3 j
are coplanar. k, b i j, and c 7i 3j 1, 2 , and S 6, 2, 8 lie in the same points Q and R. Show that the distance d from the point P
to the line L is
ab
d
a
l
l
where a QR and b QP.
(b) Use the formula in part (a) to ﬁnd the distance from
the point P 1, 1, 1 to the line through Q 0, 6, 8 and
R 1, 4, 7 .
40. (a) Let P be a point not on the plane that passes through the points Q, R, and S. Show that the distance d from P to the
plane is
abc
d
ab 41. Prove that a b a b b. 2a 42. Prove part 6 of Theorem 8, that is, 35. A bicycle pedal is pushed by a foot with a 60N force as a shown. The shaft of the pedal is 18 cm long. Find the
magnitude of the torque about P. b c a cb a bc 43. Use Exercise 42 to prove that a
60 N v. In what l
l
l
where a QR, b QS, and c QP.
(b) Use the formula in part (a) to ﬁnd the distance from the
point P 2, 1, 4 to the plane through the points Q 1, 0, 0 ,
R 0, 2, 0 , and S 0, 0, 3 . 2k 34. Use the scalar triple product to determine whether the points P 1, 0, 1 , Q 2, 4, 6 , R 3,
plane. 857 39. (a) Let P be a point not on the line L that passes through the R 5, 2, 2 ■ ❙❙❙❙ b c b c a c a b 0 44. Prove that 70° a
10° b c acbc
adbd d P
45. Suppose that a 0.
(a) If a b a c, does it follow that b c?
(b) If a b a c, does it follow that b c?
(c) If a b a c and a b a c, does it follow
that b c? 36. Find the magnitude of the torque about P if a 36lb force is applied as shown.
P 4 ft 46. If v1, v2, and v3 are noncoplanar vectors, let k1 4 ft 37. A wrench 30 cm long lies along the positive yaxis and grips a 38. Let v v3
v2
k3 30°
36 lb bolt at the origin. A f...
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This note was uploaded on 02/04/2010 for the course M 56435 taught by Professor Hamrick during the Fall '09 term at University of Texas.
 Fall '09
 hamrick

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