Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT2024MathematicsThree Dimensional GeometryActual

Let the acute angle bisector of the two planes x-2 y-2 z+1=0 and 2 x-3 y-6 z+1=0 be the plane P . Then which of the following points lies on P?

Options

  1. A(3,1,- 1 2 )
  2. B(-2,0,- 1 2 )
  3. C(0,2,-4)
  4. D(4,0,-2)

Correct answer

B. (-2,0,- 1 2 )

Step-by-step solution

Given that P₁: x-2 y-2 z+1=0P₂: 2 x-3 y-6 z+1=0 Equation of plane bisectors aligned & | x-2 y-2 z+1 1+4+4 |= | 2 x-3 y-6 z+1 2^2+3^2+6^2 | & x-2 y-2 z+1 3 = 2 x-3 y-6 z+1 7 aligned Since a ₁ a ₂+ b ₁ ~b ₂+ c ₁ c ₂=20 0 Negative sign will be taken for acute bisector. aligned & 7 x-14 y-14 z+7=-[6 x-9 y-18 z+3] & 13 x-23 y-32 z+10=0 & (-2,0,- 1 2 ) satisfy it aligned

Practice Three Dimensional Geometry on Quantrex Academy →

More from Three Dimensional Geometry

The magnitude of projection of line joining (3,4 , 5) and (4,6,3) on the line joining (-1,2,4) and (1,0,5) is 2024The angle between the lines whose direction cosines are given by the equations 3 l+m+5 n=0,6 ~nm -2 n l+5 l m =0 is 2024Let the foot of perpendicular from a point P (1,2,-1) to the straight line L : x 1 = y 0 = z -1 be N . Let a line be drawn from P parallel to the plane x+y+2 z=0 which meets L at p 2024If the co-ordinates of the point in which the line joining the points (3,5,-7) and (-2,1,8) is intersected by the plane y z is [ a , 13 ~b , c ] , then (a+b-c)= 2023If the straight lines x-1 k = y-2 2 = z-3 3 and x-2 3 = y-3 k = z-1 2 intersect at a point, then the integer k is equal to 2023The shortest distance between the lines x = y +2=6 z-6 and x+1=2 y=-12 z is 2023The ratio in which the YZ-plane divide the line segment formed by joining the points (-2,4,7) and (3,-5,8) is 2: m . The value of m is 2023The lines x-2 1 = y-3 1 = z-4 -k and x-1 k = y-4 2 = z-5 1 are coplanar if 2023 Full Three Dimensional Geometry list All BITSAT PYQs