Question

Assertion :Consider the planes $3x-6y-2z=15$ and $2x+y-2z=5$.
STATEMENT -1 : The parametric equations of the line of intersection of the given planes are $x=3+14t$,
$y=1+2t,z=15t$ Reason: STATEMENT -2: The vectors $14i+2\hat{j}+15\hat{k}$ is parallel to the line of intersection ofthe given planes.

• A. Statement -1 is True, Statement -2 is True; Statement-2 is a correct explanation for Statement-1
• B. Statement -1 is True, Statement -2 is True; Statement-2 is NOT a correct explanation for Statement-1
• C. Statement -1 is True, Statement -2 is False
• D. Statement -1 is False, Statement -2 is True

Answer 1

The correct option is D Statement -1 is False, Statement -2 is True

$3x-6y-2z=15$
$2x+y-2z=5$
for $z=0$, we get $x=3,y=-1$
$D$irection vectors of plane are
$<3$ $-6$ $-2>$ and $<2$ $1$ $-2>$
then the $dr$'s of line of intersection of planes is $<14$ $2$ $15>$
$\frac{x-3}{14}=\frac{y+1}{2}=\frac{z-0}{15}=\lambda$
$\Rightarrow x=14\lambda +3,$
$y=2\lambda -1,$
$z=15\lambda$
Hence, statement 1 is false.But statement 2 is true.