Question

Consider the planes $3x-6y-2z=15$ and $2x+y-2z=5.$

Assertion: The parametric equations of the line of intersection of the given planes are $x=3+14t,y=1+2t,z=15t.$ because

Reason: The vector $14\hat{i}+2\hat{j}+15\hat{k}$ 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

$3x-6y-2z=15$

$2x+y-2z=5$

For $z=0$ we get $x=3,y=-1$

Direction vectors of plane are $<3-6-2>$ and $<2,1,-2>$

Then the dr's of line of intersection of planes is $<14,2,15>$

$\therefore \frac{x-3}{14}=\frac{y+1}{2}=\frac{z-0}{15}=\lambda$

$⟹x=14\lambda +3y=2\lambda -1z=15\lambda$

hence Both Assertion and Reason are incorrect