Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202620 April 2026Morning ShiftMathematicsThree Dimensional GeometryActual

The shortest distance between the lines x - 3 3 = y - 8 -1 = z - 3 1 and x + 3 -3 = y + 7 2 = z - 6 4 is

Options

  1. A5 30
  2. B3 30
  3. C2 30
  4. D30

Correct answer

B. 3 30

Step-by-step solution

The given lines are: L₁: x - 3 3 = y - 8 -1 = z - 3 1 L₂: x + 3 -3 = y + 7 2 = z - 6 4 The position vectors of points on the lines are a ₁ = 3 i + 8 j + 3 k and a ₂ = -3 i - 7 j + 6 k . The direction vectors of the lines are b ₁ = 3 i - j + k and b ₂ = -3 i + 2 j + 4 k . The shortest distance d between two skew lines is given by: d = |( a ₂ - a ₁) ( b ₁ b ₂)| | b ₁ b ₂| First, finding a ₂ - a ₁ : a ₂ - a ₁ = (-3 - 3) i + (-7 - 8) j + (6 - 3) k = -6 i - 15 j + 3 k Next, finding b ₁ b ₂ : b ₁ b ₂ = vmatrix i & j & k

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