Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202313 May 2023Evening ShiftMathematicsThree Dimensional GeometryActual

A tetrahedron has vertices at P (2,1,3) , Q (-1,1,2), R (1,2,1) and O (0,0,0) , then angle between the faces OPQ and PQR is

Options

  1. A⁻¹ ( 5 7 59 )
  2. B⁻¹ ( 25 59 35 )
  3. C⁻¹ ( 5 413 )
  4. D⁻¹ ( 25 59 35 )

Correct answer

D. ⁻¹ ( 25 59 35 )

Step-by-step solution

aligned O P O Q & = | array ccc i & j & k 2 & 1 & 3 -1 & 1 & 2 array | & =- i -7 j +3 k aligned aligned P Q P R & = | array ccc i & j & k -3 & 0 & -1 -1 & 1 & -2 array | & = i -5 j -3 k aligned Angle between the faces OPQ and PQR is = (- i -7 j +3 k ) ( i -5 j -3 k ) (-1)^2+(-7)^2+3^2 1^2+(-5)^2+(-3)^2 = -1+35-9 59 35 aligned & = 25 59 35 & = ⁻¹ ( 25 59 35 ) aligned

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