Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202225 Jun 2022Morning ShiftMathematicsThree Dimensional GeometryActual

Let Q be the mirror image of the point P 1 , 0 , 1 with respect to the plane S : x + y + z = 5 . If a line L passing through 1 , - 1 , - 1 , parallel to the line P Q meets the plane S at R , then Q R 2 is equal to

Options

  1. A2
  2. B5
  3. C7
  4. D11

Correct answer

B. 5

Step-by-step solution

Let parallel vector of L = Let Q a , b , c As Q is the mirror image on given plane x + y + z = 5 so a - 1 1 = b - 0 1 = c - 1 1 = - 2 2 - 5 3 a = 3 , b = 2 , c = 3 i.e. Q ≡ 3 , 2 , 3 Let the vector parallel to L be b → So, b → = 1 , 1 , 1 Equation of line L : x - 1 1 = y + 1 1 = z + 1 1 Let point R λ + 1 , λ - 1 , λ - 1 is lying on plane x + y + z = 5 , so, 3 λ - 1 = 5 ⇒ λ = 2 So, point R is 3 , 1 , 1 Hence, Q R 2 = 5

Practice Three Dimensional Geometry on Quantrex Academy →

More from Three Dimensional Geometry

Let P be the plane such that it contains the straight line x-1 2 = y-3 3 = z+2 1 and is perpendicular to the plane x + 2y + 3z = 4 . Let P₁ be the plane which passes through the po 2026Let L be the straight line joining the points P(1, 2, -1) and Q(2, 3, 1) . Let S be the foot of the perpendicular drawn from the point R(4, -1, 5) to the line L . Another line pass 2026Let the foot of perpendicular from the point ( , 2, 3) on the line x-4 1 = y-9 2 = z-5 1 be the point (1, , 2) . Then the distance between the lines x-1 2 = y-2 3 = z+4 6 and x- 2 2026Let a line L₁ pass through the origin and be perpendicular to the lines L₂: r = (3+t) i + (2t-1) j + (2t+4) k and L₃: r = (3+2s) i + (3+2s) j + (2+s) k , t, s R . If (a, b, c) , a 2026The shortest distance between the lines x-4 1 = y-3 2 = z-2 -3 and x+2 2 = y-6 4 = z-5 -5 is : 2026Let the image of the point P(0, -5, 0) in the line x-1 2 = y 1 = z+1 -2 be the point R and the image of the point Q (0, -1 2 , 0 ) in the line x-1 -1 = y+9 4 = z+1 1 be the point S 2026Let the image of the point P(1, 6, a) in the line L: x 1 = y-1 2 = z-a+1 b , b > 0 , be ( a 3 , 0, a+c ) . If S( , , ) , > 0 , is the point on L such that the distance of S from th 2026Let a line L be perpendicular to both the lines L₁: x+1 3 = y+3 5 = z+5 7 and L₂: x-2 1 = y-4 4 = z-6 7 . If is the acute angle between the lines L and L₃: x - 8 7 2 = y - 4 7 1 = 2026 Full Three Dimensional Geometry list All JEE Main PYQs