JEE Main 2022 · 28 Jul · Shift 2 · Mathematics Q75

← JEE Main 2022 · 28 Jul · Shift 2

MathematicsSingle correct+4 / -1Question 75 of 90

Let the lines $\dfrac{x-1}\lambda=\dfrac{y-2}1=\dfrac{z-3}2$ and $\dfrac{x+26}{-2}=\dfrac{y+18}3=\dfrac{z+28}\lambda$ be coplanar and P be the plane containing these two lines. Then which of the following points does NOT lie on P?

(0, −2, −2)

(−5, 0, −1)

(3, −1, 0)

(0, 4, 5)

Answer and worked solution

Official answer: D

Coplanar. The determinant of $(-27,-20,-31)$ , $(\lambda,1,2)$ , $(-2,3,\lambda)$ vanishes only at $\lambda=3$ .

Plane. Normal $(3,1,2)\times(-2,3,3)=(-3,-13,11)$ through (1, 2, 3): $3x+13y-11z=-4$ .

Check. (0, 4, 5) gives $52-55=-3\ne-4$ , so it is not on P. (D)

Topics:Equation of a plane Skew lines

← Previous question Next question →

JEE Main 2022 · 28 Jul · Shift 2, Mathematics question 75