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The line L1 is given by (x-1)/2 = (y-1)/(-1) = z/2. The line L2 is the intersection of the planes x - y + z - 2 = 0 and lambda*x + 3z + 5 = 0. If L1 and L2 are coplanar, find [|lambda|], where [ ] denotes the greatest integer function.
- 3
- 4
- 5
- 6
Correct answer: 4
Solution
The direction of L2 is n1 x n2 = (-3, lambda-3, lambda). Taking a point on L1 as (1,1,0) and a point on L2 by setting z=0 in both plane equations, the coplanarity condition (scalar triple product = 0) gives 9*lambda + 37 = 0, so lambda = -37/9. Then |lambda| = 37/9 ≈ 4.11, and [|lambda|] = 4.
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