Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202017 Sep 2020Morning ShiftMathematicsThree Dimensional GeometryActual

The direction cosines of the line which is perpendicular to the lines with direction cosines proportional to ( 1,-2,-2 ) and ( 0,2,1 ) is given by

Options

  1. A( 2 3 , 1 3 , 2 3 )
  2. B( -2 3 , -1 3 , -2 3 )
  3. C( 2 3 , 1 3 , -2 3 )
  4. D( 2 3 , -1 3 , 2 3 )

Correct answer

D. ( 2 3 , -1 3 , 2 3 )

Step-by-step solution

Let (l, m, n ) be the direction cosines of the required line. Since, it is perpendicular to the lines whose direction cosines are proportional to (1,-2,-2 ) and (0,2,1 ) respectively Thus, (l-2 m-2 n=0 ) and (2 m+n=0 ) On solving ( 1 2 = m -1 = n 2 ) Thus, DR's of required line are proportional to ((2,-1,2) ) Hence, direction cosines are (= ( 2 3 ,- 1 3 , 2 3 ) )

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