Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET20239 May 2023Evening ShiftMathematicsThree Dimensional GeometryActual

The co-ordinates of the point, where the line x-1 2 = y-2 -3 = z+5 4 meets the plane 2 x+4 y-z=3 , are

Options

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

Correct answer

A. (3,-1,-1)

Step-by-step solution

Given line is x-1 2 = y-2 -3 = z+5 4 Let x-1 2 = y-2 -3 = z+5 4 = array ll & x-1=2 , y-2=-3 , z +5=4 & x=2 +1, y=-3 +2, z =4 -5 & 2 x+4 y- z =3 & 2(2 +1)+4(-3 +2)-(4 -5)=3 & 4 +2-12 +8-4 +5=3 & -12 =3-15 & =1 & x=3, y=-1, z =-1, array Required co-ordinates are: (3,-1,-1)

Practice Three Dimensional Geometry on Quantrex Academy →

More from Three Dimensional Geometry

The circum radius of the triangle formed by the points (2,-1,1),(1,-3,-5) and (3,-4,-4) is 2025Let A (2,3,5), B (-1,3,2), C ( , 5, ) be the vertices of ABC . If the median through the vertex A is equally inclined to the coordinate axes, then 2025Equation of the plane passing through the origin and perpendicular to the planes x+2 y-z=1 and 3 x-4 y+z=5 is 2025If the line joining the points i +2 j and j -2 k intersects the plane passing through the points 2 i - j , 2 j +3 k and k -2 i at r , then r ( i + j + k )= 2025The vector equation of a plane passing through the line of intersection of the planes r ( i -2 k )=3, r (2 j + k )=5 and the point i +2 j +3 k is 2025The points A (-1,2,3), B (2,-3,1), C (3,1,-2) 2025The direction cosines of the line making angles 4 , 3 and (0 < < 2 ) respectively with X , Y and Z axes are 2025If the equation of the plane passing through the point (3,2,5) and perpendicular to the planes 2 x-3 y+5 z=7 and 5 x+2 y-3 z=11 is x+b y+c z+d=0 , then 2 b+3 c+d= 2025 Full Three Dimensional Geometry list All MHT CET PYQs