Question

The equations of the straight line through the origin and parallel to the line (b + c)x + (c + a)y + (a + b)z = k = (b – c)x + (c – a)y + (a – b)z are

• A. $\frac { x } { b ^ { 2 } - c ^ { 2 } } = \frac { y } { c ^ { 2 } - a ^ { 2 } } = \frac { z } { a ^ { 2 } - b ^ { 2 } }$
• B. $\frac { x } { b } = \frac { y } { c } = \frac { z } { a }$
• C. $\frac { x } { a ^ { 2 } - b c } = \frac { y } { b ^ { 2 } - c a } = \frac { z } { c ^ { 2 } - a b }$
• D. None of these

Answer 1

Answer: (C)

$\frac { x } { a ^ { 2 } - b c } = \frac { y } { b ^ { 2 } - c a } = \frac { z } { c ^ { 2 } - a b }$

Answer 2

Equations of straight line through the origin are

where l((b+c) + m(c+a) + n(a + b) = 0

and l(b − c) + m(c −a) + n(a − b) = 0.

On solving,

Equations of the straight line are$\frac { x } { a ^ { 2 } - b c } = \frac { y } { b ^ { 2 } - c a } = \frac { z } { c ^ { 2 } - a b }$