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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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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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