Let Q be the mirror image of the point P 1 , 2 , 1 with respect to the plane x + 2 y + 2 z = 16 . Let T be a plane passing through the point Q and contains the line r → = - k ^ + λ ( i ^ + j ^ + 2 k ^ ) , λ ∈ R . Then, which of the following points lies on T ?

Question

Let Q be the mirror image of the point P 1 , 2 , 1 with respect to the plane x + 2 y + 2 z = 16 . Let T be a plane passing through the point Q and contains the line r → = - k ^ + λ ( i ^ + j ^ + 2 k ^ ) , λ ∈ R . Then, which of the following points lies on T ?, 2 , 1 , 0, 1 , 2 , 1, 1 , 2 , 2, 1 , 3 , 2

MARKS App · Accepted Answer

We know that by image formula, image of P 1 , 2 , 1 in x + 2 y + 2 z - 16 = 0 is given by Q 4 , 8 , 7 Now equation of plane will be given by T = x - x 1 y - y 1 z - z 1 a 1 b 1 c 1 a 2 b 2 c 2 = 0 ⇒ T = x - 0 y - 0 z + 1 4 - 0 8 - 0 7 + 1 1 1 2 = 0 ⇒ 2 x - z = 1 Now from options, only point B 1 , 2 , 1 lies on it.

Search any question & find its solution

Looking for more such questions to practice?