Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT2017MathematicsThree Dimensional GeometryActual

The distances of the point ( 1 , - 5 , 9 ) from the plane x + y + z = 5 measured along a straight line x = y = z is 2 3 k , then the value of k is

Options

  1. A5
  2. B6
  3. C3
  4. D4

Correct answer

A. 5

Step-by-step solution

Given equation of plane is x + y + z = 5 . The distance measured along the line x = y = z . Direction ratios of the given line is ( 1 , 1 , 1 ) . So, the equation of line P Q is x - 1 1 = y + 5 1 = z - 9 1 = λ ⇒   x = λ + 1 , y = λ - 5 , z = λ + 9 lies on the plane x + y + z = 5 ∴   ( λ + 1 ) - ( - λ + 5 ) + ( λ + 9 ) = 5 ⇒   λ = - 10 The coordinate of Q is ( - 9 , - 15 , - 1 ) and the coordinate of P is ( 1 , - 5 , 9 ) P Q = ( 10 ) 2 + ( 10 )

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 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? 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 2023 Full Three Dimensional Geometry list All BITSAT PYQs