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Let vectors a, b, c be defined in component form, and suppose the scalar triple product [3a + b, 3b + c, 3c + a] = lambda * [a b c], where [a b c] denotes the scalar triple product (determinant of the matrix with rows a, b, c). Find the value of lambda / 4.
- 3
- 4
- 5
- 7
Correct answer: 7
Solution
Expanding [3a+b, 3b+c, 3c+a] by multilinearity, the nonzero contributions come from choosing one vector from each slot such that all three are different. The net coefficient of [a,b,c] comes out to 27 (from 3a,3b,3c) + 1 (from b,c,a) = 28. So lambda = 28 and lambda/4 = 7.
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