Question

If the plane ax – by + cz = 0 contains the line (x – a)/a = (y – 2d)/b = (z – c)/c, find the value of (b/d).

Answer 1

Given plane is

ax – by + c z = 0 ....(i)

and the line is

Since the plane (i), contains the line (ii), so,

a(a) – b(b) + c (c) = 0

a(a) – b(2d) + c (c) = 0 

a² + c² = b²

a² + c² = 2bd

Clearly, b² = 2bd

= b/d = 2