JEE Advanced | 2018Trigonometric EquationHard

Question

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 ?

Options

A.

The line of intersection of P1 and P2 has direction ratios 1, 2, –1

B.

The line 3x-49=1-3y9=z3 is perpendicular to the line of intersection of P1 and P2

C.

The acute angle between P1 and P2 is 60°

D.

If P3 is the plane passing through the point (4, 2, –2) and perpendicular to the line of  intersection of P1 and P2, then the distance of the point (2, 1, 1) from the plane P2 is23

Solution

D.C. of line of intersection (a, b, c)
⇒2a + b – c = 0
a + 2b + c = 0
a1+2=b-1-2=c4-1∴D.C is (1,-1,1)
 (B) 3x-49=1-3y9=z3⇒x-4/33=y-1/3-3=z3
⇒lines are parallel.
(C) Acute angle between P1 and P2 =cos-12×1+1×2-1×166
=cos-136=cos-112=60o
(D) Plane is given by (x – 4) – (y – 2) + (z + 2) = 0
⇒x – y + z = 0
Distance of (2, 1, 1) from plane =2-1+13=23

Create a free account to view solution

View Solution Free
Topic: Trigonometric Equation·Practice all Trigonometric Equation questions

More Trigonometric Equation Questions

The values of θ lying between θ = 0 and θ = π / 2 and satisfing the equation is,...Locus of centroid of the triangle whose vertices are (a cos t, a sin t), (b sin t, - b cos t) and (1, 0), where t is a p...Let A and B denote the statements A : cosα + cosβ + cosγ = 0 B : sinα + sinβ + sinγ = 0 If...Which of the following is/are correct -...The most general solutions of the equation sec x - 1 = (√2-1) tan x are given by -...