Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET20249 May 2024Morning ShiftMathematicsThree Dimensional GeometryActual

The length of the perpendicular from the point A (1,-2,-3) on the line x-1 2 = y+3 -1 = z+1 -2 is

Options

  1. A6 units
  2. B3 units
  3. C2 units
  4. D4 units

Correct answer

C. 2 units

Step-by-step solution

Let x-1 2 = y+3 -1 = z+1 -2 = Any general point on this line is Q (2 +1,- -3,-2 -1) The direction ratios of AQ are 2 ,- -1,-2 +2 Since A Q is perpendicular to given lines. aligned & 2(2 )-1(- -1)-2(-2 +2)=0 & 4 + +1+4 -4=0 & 9 -3=0 & = 1 3 & Q ( 5 3 , -10 3 , -5 3 ) aligned AQ = (1- 5 3 )^2- (-2+ 10 3 )^2+ (-3+ 5 3 )^2 aligned & = 4 9 + 16 9 + 16 9 = 36 9 = 4 A Q & =2 units 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