Discussion Forum

1)

 If the line  $r= (\hat{i}-2\hat{j}+3\hat{k})+\lambda (2\hat{i}+\hat{j}+2\hat{k})$    is parallel to the plane

$r. (3\hat{i}-2\hat{j}+m\hat{k})=10$ , then the value of m is 

Answer:

Option A

Explanation:

Given line, 

           $r= (\hat{i}-2\hat{j}+3\hat{k})+\lambda (2\hat{i}+\hat{j}+2\hat{k})$    is parallel to the plane

$r. (3\hat{i}-2\hat{j}+m\hat{k})=0$

we know that, if line r= a+$\lambda$.b is parallel to plane  r.n=d

 then , b.n=0

 $\therefore$    $(2\hat{i}+\hat{j}+2\hat{k}) .(3\hat{i}-2\hat{j}+m\hat{k}) =0  $

 6-2+2m=0

    m=-2