Question

Following question contains statements given in two columns, which have to be matched. The statements inColumn-I are labelled as A, B, C and D while the statements in Column-II are labelled as p, q, r and s. Any given statement in Column-I can have correct matching with ONE OR MORE statement(s) in Column-II.

Match the following pair of planes with their lines of intersections

Answer 1

(A) Vector parallel to line of intersection of the plane is $(\hat{i}+\hat{j})\times (\hat{j}+\hat{k})=\hat{k}-\hat{j}+\hat{i}$

equation of line whose dr's, are $(1,-1,1)$ and passing through $(0,0,0)$ is

$x=-y=z$

(B) Similarly $(\hat{i}\times \hat{j})=\hat{k}$

Hence dr's $=(0,0,1)$

and passing through the point $(2,3,0)$

$\therefore$ Equation of line $\frac{x-2}{0}=\frac{y-3}{0}=\frac{z}{1}$

(C) Similarly $\hat{i}\times (\hat{j}+\hat{k})=\hat{k}-\hat{j}$
dr's $=(0,-1,1)$

Equation of line $\frac{x-2}{0}=\frac{y-2007}{-1}=\frac{z+2004}{1}$

because $x=2$ & $y+z=3$

so $y=2007,z=-2004$ satisfy above equation

(D) $x=2,x+y+z=3$

$y+z=1$ same as part C

We get $\frac{x-2}{0}=\frac{y}{-1}=\frac{z-1}{1}$