HW5-510-soln - AMS 510 HW5 Solution NOTE all of UPPERCASE...

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AMS 510 HW5 Solution NOTE: all of UPPERCASE letters denote vectors, A means A , AB means AB ; all of lowercase letters denote scalar, except i, j, k. 7.55 2i 3 j 6 k  3i aj – 2 k = 0 a =− 4 / 3 7.56 A C = 5i 3 j 3 k A C ⋅ B B = 17 / 3 7.57 (a) point D's coordinate is A C 2 D 3 / 2,1 / 2,2  ⇒ BD = 3 / 2i 1 / 2j 2k BD ∣= 26 / 2 (b) BC = 2i 3 j k cos = BD BC BD ∣⋅∣ BC = 91 / 14 ⇒ = cos 1 91 / 14 7.61 suppose N = xi yj zk { N A = 0 N B = 0 N ∣= 1 { x = 0 y = 1 / 5 z = 1 / 5 , { x = 0 y =− 1 / 5 z =− 1 / 5 N =± 2 / 5 j 1 / 5 k 7.63 BA = A – B = i 2 j – k ,BC = C B =− 2i 3j k s = 1 2 BA × BC ∣= 1 2 ∣∣ i j k 1 2 1 2 3 1 ∣∣ = 1 2 i j k ∣= 3 / 2 7.64 if A(3,2,1), B(1,1,0), C(3,-1,1), D(-1,0,2)
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the volume formed by ABCD is v = 1 6 AB ⋅ AC × AD = 1 6 ∣∣ 2
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HW5-510-soln - AMS 510 HW5 Solution NOTE all of UPPERCASE...

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