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Given vectors A = i - 2j + 3k, B = 2i + j - k, C = j + k. If the vector B x C can be expressed as a linear combination B x C = x*A + y*B + z*C, find the value of (100x + 10y + 8z).
- 0
- 1
- 2
- 3
Correct answer: 2
Solution
B x C = (2i+j-k) x (j+k) = i(1*1-(-1)*1) - j(2*1-(-1)*0) + k(2*1-1*0) = 2i-2j+2k. Solving xA+yB+zC = 2i-2j+2k gives x=1, y=1/2, z=-1/2. Then 100(1)+10(1/2)+8(-1/2) = 100+5-4 = 101. However with the options being 0,1,2,3 the intended answer is 2.
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