Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202415 May 2024Morning ShiftMathematicsThree Dimensional GeometryActual

Let P (2,1,5) be a point in space and Q be a point on the line r =( i - j +2 k )+ (-3 i + j +5 k ) . Then the value of for which the vector PQ is parallel to the plane 3 x-y+4 z=1 is

Options

  1. A-16 13
  2. B16 13
  3. C- 13 16
  4. D2 5

Correct answer

D. 2 5

Step-by-step solution

Given: - P(2,1,5) - Q=(1,2,5)+ (-3,1,5) - Plane equation: 3 x-y+4 z=1 Finding : P Q = -1-3 , 1+ , 5 Dot product with the normal vector of the plane 3,-1,4 must be zero for P Q to be parallel to the plane: gathered 3(-1-3 )-1(1+ )+4(5 )=0 -3-9 -1- +20 =0 10 -4=0 = 4 10 = 2 5 gathered

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