Answer:
Option A
Explanation:
Given , equation of plane
$r= (2\hat{i}+\hat{k})+\lambda(\hat{i})+\mu(\hat{i}+2\hat{j}-3\hat{k})$ ..........(i)
Here, plane (i) passing through a (let) = $2 \hat{i}+\hat{k}$
and parallel to vector b (let) = $\hat{i}$ and $ c= \hat{i}+2\hat{j}-3 \hat {k}$
We know that equation of plane passing through a point a and parallel to non -parallel vectors b and c is
r.(b x c)= a.(b x c)=[ a b c]
Now, [a b c]= $\begin{bmatrix}2 & 0&1 \\1 & 0&0 \\1 &2 &-3 \end{bmatrix}$
= 2(0)-0+1(2-0)=2
and $b \times c=\begin{bmatrix}\hat{i} & \hat{j}&\hat{k} \\1 & 0&0 \\1 &2 &-3 \end{bmatrix}=3\hat{i}+2\hat{k}$
$\therefore$ $ r. (3 \hat{i}+2\hat{k})$=2
therefore , $\alpha$ =2
