Let P 1 :   2 x   +   y   -   z   =   3   a n d   P 2 :  …

Let P1: 2x + y - z = 3 and P2: x + 2y + z = 2 be two planes. Then, which of the following statement(s) is (are) TRUE?
  1. The line of intersection of P1 , P2 has direction ratios 1, 2,-1
  2. The line 3x-49=1-3y9=z3 is perpendicular to the line of intersection of P1 ,P2
  3. The acute angle between P1 , P2 is  60o
  4. If P3 is the plane passing through the point 4, 2,-2 and perpendicular to the line of intersection of P1 , P2 , then the distance of the point 2,1,1 from the plane P3 is23

Solution

D.C of line intersection a, b, c
⇒  2a+b-c=0
a+2b+c=0
a1+2=b-1-2=c4-1
∴D.C  1, -1, 1
B 3x-49=1-3y9=z3
⇒ x-433=y-13-3=z3
⇒  lines are parallel
(C) Acute angle between P1 , P2=cos-12×1+1×2-1×166
= cos-136=cos-112=60°
D Plane is given by x-4-y-2+z+2=0
⇒  x-y+z=0
Distance of2,2,1 from plane =2-1+13=23

Asked in: JEE Advanced 2018 (Paper 1)

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