Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202317 May 2023Morning ShiftMathematicsThree Dimensional GeometryActual

Coordinate planes and the planes ₁, ₂, ₃ which are respectively parallel to YZ , ZX , XY planes at distances a , b , c , form a rectangular parallelpiped, d ₁ is a diagonal of the face on XY -plane not passing through origin and d ₂ is diagonal of plane ₂ coterminous with d ₁ . If none of the coordinates of the vertices of the parallelpiped are negative and angle between d ₁ and d ₂ is , then =

Options

  1. Aa^2 a^2+b^2 a^2+c^2
  2. Ba a^2+b^2+c^2
  3. C2
  4. Da ^2 a ^2+ b ^2 b ^2+ c ^2

Correct answer

A. a^2 a^2+b^2 a^2+c^2

Step-by-step solution

According to question d ₁=a i +b j and d ₂=a i +c j Angle between d ₁ and d ₂= d ₁ d ₂ | d ₁ | d ₂ | = a^2 a^2+b^2 a^2+c^2

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 AP EAMCET PYQs