Question

$a=2i-j+k,b=i+2j-3k,c=3i+\lambda j+5k$ are coplanar. Then find the value of $\lambda$

• A. $\lambda =4$
• B. $\lambda =-4$
• C. $\lambda =-7$
• D. $\lambda =7$

Answer 1

The correct option is B $\lambda =-4$

Three vectors, a, b, c are coplanar if $\left[abc\right]=0$
or $\left|\begin{array}{ccc}2& -1& 1\\ 1& 2& -3\\ 3& \lambda & 5\end{array}\right|=0$
or $2(10+3\lambda )+1(5+9)+1(\lambda -6)=0$ ( expanding along first row.)
or $7\lambda +28=0\therefore \lambda =-4$