JEE Main20246 Apr 2024Morning ShiftMathematicsThree Dimensional GeometryActual

The shortest distance between the lines x-3 2 = y+15 -7 = z-9 5 and x+1 2 = y-1 1 = z-9 -3 is

Options

A8 3
B4 3
C5 3
D6 3

Correct answer

B. 4 3

Step-by-step solution

aligned & x-3 2 = y+15 -7 = z-9 5 & x+1 2 = y-1 1 = z-9 -3 & S.D = | ( a ₂ a ₁ ) ( b ₁ b ₂ ) | | b ₁ b ₂ | & a₁=3,-15,9 & ~b ₁=2,-7,5 & a ₂=-1,1,9 & ~b ₂=2,1,-3 & a₂-a₁=-4,16,0 & b ₁ b ₂= | array ccc i & j & k 2 & -7 & 5 2 & 1 & -3 array |= i (16)- j (-16)+ k (16) & 16( i + j + k ) & | b ₁ b ₂ |=16 3 & ( a ₂- a ₁ ) ( b ₁- b ₂ )=16[-4+16]=(16)(12) & S.D. = (16)(12) 16 3 =4 3 & aligned

Practice Three Dimensional Geometry on Quantrex Academy →

More from Three Dimensional Geometry

Let P be the plane such that it contains the straight line x-1 2 = y-3 3 = z+2 1 and is perpendicular to the plane x + 2y + 3z = 4 . Let P₁ be the plane which passes through the po 2026 Let L be the straight line joining the points P(1, 2, -1) and Q(2, 3, 1) . Let S be the foot of the perpendicular drawn from the point R(4, -1, 5) to the line L . Another line pass 2026 Let the foot of perpendicular from the point ( , 2, 3) on the line x-4 1 = y-9 2 = z-5 1 be the point (1, , 2) . Then the distance between the lines x-1 2 = y-2 3 = z+4 6 and x- 2 2026 Let a line L₁ pass through the origin and be perpendicular to the lines L₂: r = (3+t) i + (2t-1) j + (2t+4) k and L₃: r = (3+2s) i + (3+2s) j + (2+s) k , t, s R . If (a, b, c) , a 2026 The shortest distance between the lines x-4 1 = y-3 2 = z-2 -3 and x+2 2 = y-6 4 = z-5 -5 is : 2026 Let the image of the point P(0, -5, 0) in the line x-1 2 = y 1 = z+1 -2 be the point R and the image of the point Q (0, -1 2 , 0 ) in the line x-1 -1 = y+9 4 = z+1 1 be the point S 2026 Let the image of the point P(1, 6, a) in the line L: x 1 = y-1 2 = z-a+1 b , b > 0 , be ( a 3 , 0, a+c ) . If S( , , ) , > 0 , is the point on L such that the distance of S from th 2026 Let a line L be perpendicular to both the lines L₁: x+1 3 = y+3 5 = z+5 7 and L₂: x-2 1 = y-4 4 = z-6 7 . If is the acute angle between the lines L and L₃: x - 8 7 2 = y - 4 7 1 = 2026 Full Three Dimensional Geometry list All JEE Main PYQs