Question

Assertion :Consider the planes $3x-6y-2z=15$ and $2x+y-2z=5$
Statement-1: The parametric equation of the line of intersection of the given planes are $x=3+14t,y=1+2t,z=15t$ Reason: Statement-2: The vector $14i+2j+15k$ is parallel to the line of intersection of given planes

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is D Both Assertion and Reason are incorrect

We have $3(3+14t)-6(1+2t)-2\left(25t\right)$
$=9+42t-6-12t-12t-30t=3\ne 0$
Thus the line $x=3+14t,y=1+2t,z=15t$ does not lie on the plane $3x-6y-2z=15$
$\therefore x=3+14t,y=1+2t,z=15t$ cannot be the line of intersection of the planes.
$\Rightarrow 3x-6y-2z=15$ and $2x+y-2z=5$
Since $3\left(14\right)-6\left(2\right)-2\left(15\right)=0$ and $2\left(14\right)+1\left(2\right)-2\left(15\right)=0$,
So the vector $14i+2j+15k$ is perpendicular to the line of intersection of the two planes.