Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET2001MathematicsThree Dimensional Geometry

The foot of the perpendicular from (0,2,3) to the line x+3 5 = y-1 2 = z+4 3 is

Options

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

Correct answer

C. (2,3,-1)

Step-by-step solution

Let N be the foot of the perpendicular from the point P(0,2,3) on the given line x+3 5 = y-1 2 = z+4 3 =r (say) ... (i) Any point on the line (i) is (5 r-3,2 r+1,3 r-4) If this point is N , The direction ratio's of N P are 5 r-3,2 r+1-2,3 r-4-3 i.e. 5 r-3,2 r-1,3 r-7 Since, N P is perpendicular to the given line, then aligned & 5(5 r-3)+2(2 r-1)+3(3 r-7)=0 & 38 r-38=0 r=1 & The point N is (5-3,2+1,3-4) & i.e., (2,3,-1) . 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