Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202120 Aug 2021Morning ShiftMathematicsThree Dimensional GeometryActual

If the lines x - 3 2 = y - 2 3 = z - 1 λ and x - 2 3 = y - 3 2 = z - 2 3 are coplanar, then sin - 1 ( sin λ ) + cos - 1 ( cos λ ) =

Options

  1. A8 - 2 π
  2. B6 - π
  3. C3 π - 8
  4. D4 π - 8

Correct answer

C. 3 π - 8

Step-by-step solution

First line: x - 3 2 = y - 2 3 = z - 1 λ A ≡ ( 3 , 2 , 1 )   is a point on the line Direction ratios are, a → =   2 i ^ + 3 j ^ + λ k ^ Second line: x - 2 3 = y - 3 2 = z - 2 3 B ≡ ( 2 , 3 , 2 )   is a point on the line Direction ratios are, b →   =   3 i ^ + 2 j ^ + 3 k ^ A B → =   - i ^ + j ^ + k ^   ;   a → =   2 i ^ + 3 j ^ + λ k ^   ;   b →   = &#

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