Zaymiey

📐 Mathematics  ·  Three Dimensional Geometry  ·  JEE

The shortest distance between skew lines x=y=z and (x+1)/1=y/2=z/3 is:

Answer: 1/sqrt(6).

  • A 1/sqrt(6)
  • B 1/sqrt(3)
  • C 1/sqrt(2)
  • D 0

Correct answer: A. 1/sqrt(6)

Explanation: Line1: r=(0,0,0)+t(1,1,1). Line2: r=(-1,0,0)+s(1,2,3). b<sub>1</sub> x b<sub>2</sub> = (1,1,1) x (1,2,3) = (3-2,1-3,2-1) = (1,-2,1). |b<sub>1</sub> x b<sub>2</sub>| = sqrt(6). (a<sub>2</sub>-a<sub>1</sub>) = (-1,0,0). SD = |(-1,0,0).(1,-2,1)|/sqrt(6) = |-1|/sqrt(6) = 1/sqrt(6).

zxyOP (x, y, z)

Three mutually perpendicular axes x, y, z meeting at the origin O, with a point P located by its (x, y, z) coordinates.

Concept context

Lines and planes in 3D space, direction cosines, distances, and angles

Read the full Three Dimensional Geometry notes →