Question

Match the statements of Column I with values of Column II.

Answer 1

A) Since, the line lies in a plane.
Therefore, their direction ratios are perpendicular.
$3\left(1\right)-2(-2)+5\left(\lambda \right)=0$
$\Rightarrow \lambda =\frac{-7}{5}$
B) Since, the point $(3,\lambda ,\mu )$ lies in a plane

$2x+y+z-3=0=x-2y+z-1$
Therefore,

$6+\lambda +\mu -3=0\Rightarrow \lambda +\mu =-3$
C) angle between given plane and line is

${\sin }^{-1}\left(\frac{4-3+5}{\sqrt{\left((4^2+3^2+5^2)\right)(1^2+1^2+1^2)}}\right)={\sin }^{-1}\sqrt{\frac{6}{25}}$
D) angle between given planes is

${\cos }^{-1}\left(\frac{3-4+5}{\sqrt{\left((4^2+3^2+5^2)\right)(1^2+1^2+1^2)}}\right)={\cos }^{-1}\sqrt{\frac{8}{75}}$