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Let a = i + j, b = j + k, and c = alpha*a + beta*b. If the vectors (i - 2j + k), (3i + 2j - k), and c are coplanar, then |alpha/beta| equals:
- 1
- 2
- 3
- 4
Correct answer: 3
Solution
Setting up the coplanarity determinant with rows (1,-2,1), (3,2,-1), (alpha, alpha+beta, beta) and equating to zero gives 4*alpha + 12*beta = 0, so alpha/beta = -3 and |alpha/beta| = 3.
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