Zaymiey

📐 Mathematics  ·  Three Dimensional Geometry  ·  JEE

The shortest distance between the lines x=1,y=2 and y=3,z=4 (lines parallel to z-axis and x-axis respectively) is:

Answer: sqrt(5).

  • A sqrt(2)
  • B sqrt(5)
  • C sqrt(10)
  • D 1

Correct answer: B. sqrt(5)

Explanation: Line 1: (1,2,t) direction (0,0,1). Line 2: (s,3,4) direction (1,0,0). b<sub>1</sub> x b<sub>2</sub> = (0,0,1)x(1,0,0) = (0,1,0). |b<sub>1</sub> x b<sub>2</sub>|=1. (a<sub>2</sub>-a<sub>1</sub>)=(0,1,2). SD = |(0,1,2).(0,1,0)|/1 = |1| = 1. Answer is 1 (index 3).

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

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