Zaymiey

📐 Mathematics  ·  Three Dimensional Geometry  ·  JEE

Two lines are perpendicular if their direction ratios (a<sub>1</sub>,b<sub>1</sub>,c<sub>1</sub>) and (a<sub>2</sub>,b<sub>2</sub>,c<sub>2</sub>) satisfy:

Answer: a 1 a 2 + b 1 b 2 + c 1 c 2 = 0.

  • A a<sub>1</sub>/a<sub>2</sub> = b<sub>1</sub>/b<sub>2</sub> = c<sub>1</sub>/c<sub>2</sub>
  • B a<sub>1</sub>a<sub>2</sub> + b<sub>1</sub>b<sub>2</sub> + c<sub>1</sub>c<sub>2</sub> = 0
  • C a<sub>1</sub>a<sub>2</sub> = b<sub>1</sub>b<sub>2</sub>
  • D a<sub>1</sub>+a<sub>2</sub> = 0

Correct answer: B. a<sub>1</sub>a<sub>2</sub> + b<sub>1</sub>b<sub>2</sub> + c<sub>1</sub>c<sub>2</sub> = 0

Explanation: Perpendicular lines have zero dot product of direction vectors: a<sub>1</sub>a<sub>2</sub> + b<sub>1</sub>b<sub>2</sub> + c<sub>1</sub>c<sub>2</sub> = 0.

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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