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

Let L be the line passing through the points i -9 k and 7 j + k and be the plane passing through the point 6 i + j and perpendicular to the vector i + j + k . If is the angle between L and , then =

Options

  1. A8 2 15
  2. B3 3 8
  3. C7 13
  4. D24 25

Correct answer

A. 8 2 15

Step-by-step solution

aligned & L : r = a + ( b - a ) & r =( i -9 k )+ ( i -9 k -7 j - k ) & r =( i -9 k )+ ( i -7 j -10 k )...(i) & : r n = p n & r ( i + j + k )=(6 i + j ) ( i + j + k ) & r ( i + j + k )=6+1=7 aligned Here, a = i -9 k , b =( i -7 j -10 k )| n |= 1+1+1 = 3 and | b |= 1+49+100 = 150 =5 6 aligned & Now, = | n b | n | b | |= ( i + j + k ) ( i -7 j -10 k ) 3 5 6 & = | 1-7-10 3 5 2 |= 16 15 2 = 16 2 15 2 = 8 2 15 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 AP EAMCET PYQs