Question

A plane passing through the point $(3,1,1)$ contains two lines whose direction ratios are $1,-2,2$ and $2,3,-1$ respectively. If this plane also passes through the point $(\alpha ,-3,5)$, then $\alpha$ is equal to:

• A. $-5$
• B. $10$
• C. $5$
• D. $-10$

Answer 1

The correct option is C $5$

Required plane is $\left|\begin{array}{ccc}x-3& y-1& z-1\\ 1& -2& 2\\ 2& 3& -1\end{array}\right|=0$

$\Rightarrow -4(x-3)+5(y-1)+7(z-1)=0$
$\Rightarrow 4x-5y-7z=0$
$(\alpha ,-3,5)$ lies on $4x-5y-7z=0$
$\Rightarrow \alpha =5$