Question

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

• A. $\lambda =-5$
• B. $\lambda =-4$
• C. $\lambda =4$
• D. $\lambda =5$

Answer 1

Answer: (B)

$\lambda =-4$

Since, vectors are coplanar
Therefore, $\left|\begin{array}{ccc}1& -3& 1\\ 2& \lambda & 1\\ 3& 1& -2\end{array}\right|=-2\lambda -1-21+(2-3\lambda )=-5\lambda -20=0$
$\Rightarrow \lambda =-4$