Question

Assertion :Line $\frac{x-1}{3}=\frac{y-2}{11}=\frac{z+1}{11}$ lies in the plane $11x-3z-14=0$ Reason: A straight line lies in plane if the line is parallel to the plane and a point of the line lies in the plane.

• 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 A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$\frac{x-1}{3}=\frac{y-2}{11}=\frac{z+1}{11}$

$DR$ of line is $(3,11,11)$
Now taking the dot product of $DR$ and the line in the plane:

$(11,0,-3).(3,11,11)=0$ [Both the lines are parallel]

Point $(1,2,-1)$ should lie on the plane $11x-3z-14=0$

$\therefore$ Line lies in the plane.

Option A is correct.