A) \[1\]
B) \[-1\]
C) \[-4\]
D) \[4\]
Correct Answer: C
Solution :
Let \[a=2i-j+k\] \[b=i+2j-3k\] \[c=3i+\lambda j+5k\] Given, a, b and c are coplanar. \[\Rightarrow \] \[[a\,\,\,\,\,b\,\,\,\,\,c]=0\] \[\Rightarrow \] \[\left| \begin{matrix} 2 & -1 & 1 \\ 1 & 2 & -3 \\ 3 & \lambda & 5 \\ \end{matrix} \right|=0\] \[\Rightarrow \] \[2(10+3\lambda )+(5+9)+(\lambda -6)=0\] \[\Rightarrow \] \[20+6\lambda +14+\lambda -6=0\] \[\Rightarrow \] \[7\lambda +28=0\Rightarrow \lambda =-4\]
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