Question

JEE Mains Maths question is attached

Answer 1

which of the following lies on pane containing lines r = i + λ(i + j + k) and r = -j + μ(-i - 2j + k)

1. (1, 3, 6)
2. (1, -3, 6)
3. (-2, 1, 2)
4. (1, 3, 1)

normal of plane , n = (i + j + k) × (-i - 2j + k)

= (1 × 1 - (-2) × 1)i - (1 × 1 - (-1) × 1)j + (1 × -2 - (-1) × 1)k

= 3i - 2j - k

so direction ratios = (3, -2, -1)

now equation of plane = 3(x - 1) -2(y - 0) -1(z - 0) = 0

⇒3x - 3 - 2y - z = 0

⇒3x - 2y - z = 3 .......(1)

now check which point satisfies equation (1)

option (2) (1, -3, 6) :

3(1) - 2(-3) - 6 = 3 + 6 - 6 = 3 = 3

therefore point (1, - 3, 6) lies on the plane.

so the correct option is (2)