A) 0
B) 1
C) -4
D) -2
Correct Answer: D
Solution :
\[\because \]\[a=\hat{i}+\hat{j}+\hat{k},b=\hat{i}+\hat{j}+2\hat{k}\] and\[c=x\hat{i}+(x-2)\hat{j}-\hat{k}\]are coplanar. \[\therefore \] \[\left| \begin{matrix} x & x-2 & -1 \\ 1 & 1 & 1 \\ 1 & -1 & 2 \\ \end{matrix} \right|=0\] \[\Rightarrow \]\[1\{1-2(x-2)\}-1(-1-2x)+1(x-2+x)=0\] \[\Rightarrow \] \[1-2x+4+1+2x+2x-2=0\] \[\Rightarrow \] \[3x+2-x+2=0\] \[\Rightarrow \] \[2x=-4\] \[\Rightarrow \] \[x=-2\]You need to login to perform this action.
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