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Question: The equation of straight line passing through the points (a, b, c) and (a – b, b– c, c – a), is...

The equation of straight line passing through the points

(a, b, c) and (a – b, b– c, c – a), is

A

x−aa−b=y−bb−c=z−cc−a\frac { x - a } { a - b } = \frac { y - b } { b - c } = \frac { z - c } { c - a }

B

x−ab=y−bc=z−ca\frac { x - a } { b } = \frac { y - b } { c } = \frac { z - c } { a }

C

x−aa=y−bb=z−cc\frac { x - a } { a } = \frac { y - b } { b } = \frac { z - c } { c }

D

x−a2a−b=y−b2b−c=z−c2c−a\frac { x - a } { 2 a - b } = \frac { y - b } { 2 b - c } = \frac { z - c } { 2 c - a }

Answer

x−ab=y−bc=z−ca\frac { x - a } { b } = \frac { y - b } { c } = \frac { z - c } { a }

Explanation

Solution

Required line is , x−aa−b−a=y−bb−c−b=z−cc−a−c\frac { x - a } { a - b - a } = \frac { y - b } { b - c - b } = \frac { z - c } { c - a - c }

i.e., x−ab=y−bc=z−ca\frac { x - a } { b } = \frac { y - b } { c } = \frac { z - c } { a }.