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JEE Advanced2018MathematicsThree Dimensional GeometryActual

Let P 1 : 2 x + y - z = 3 a n d P 2 : x + 2 y + z = 2 be two planes. Then, which of the following statement(s) is (are) TRUE?

Options

  1. AThe line of intersection of P 1   ,   P 2 has direction ratios 1 ,   2 , - 1
  2. BThe line 3 x - 4 9 = 1 - 3 y 9 = z 3 is perpendicular to the line of intersection of P 1   , P 2
  3. CThe acute angle between P 1   ,   P 2 is   60 o
  4. DIf P 3 is the plane passing through the point 4 ,   2 , - 2 and perpendicular to the line of intersection

Correct answer

C. The acute angle between P 1   ,   P 2 is   60 o

Step-by-step solution

D.C of line intersection a ,   b ,   c ⇒     2 a + b - c = 0 a + 2 b + c = 0 a 1 + 2 = b - 1 - 2 = c 4 - 1 ∴ D . C     1 ,   - 1 ,   1 B 3 x - 4 9 = 1 - 3 y 9 = z 3 ⇒   x - 4 3 3 = y - 1 3 - 3 = z 3 ⇒   lines are parallel ( C ) Acute angle between P 1   ,   P 2 = cos - 1 2 × 1 + 1 × 2 - 1 × 1 6 6 =   cos - 1 3 6 = cos - 1 1 2 = 60 ° D Plane is given by x - 4 - y - 2 + z + 2 = 0 ⇒     x - y +

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