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Find the value of $\lambda$ for which the four points with position vectors $2\hat{i}+5\hat{j}+\hat{k},-\hat{j}-4\hat{k},3\hat{i}+\lambda\hat{j}+8\hat{k}$ and $-4\hat{i}+3\hat{j}+4\hat{k}$ are coplanar.

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2 Answers

Let the first point be A, second B, and so on... Find vector AB, vector AC, Vector AD. If three lines are coplanar, then the scalar triple product of these 3 lines must be 0. [ AB . AC. AD]=0 Solve the determinant to get the value of (lambda) Sorry, I'm new here I don't know how to make symbols and signs so couldn't elaborate much.
answered Dec 31, 2014 by nimishdelhite
construct direction vectors of all the three position vectors,solve 3*3 determinant  formed by direction ratios of all the three vectors obtained
answered Jan 1, 2015 by siddharth.sharma3

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