Question

The two lines x = ay + b, z = cy + d; and x = a'y + b', z = c'y + d' are perpendicular to each other, if

Options

• `a/a^' + c/c^' = 1`

• `a/a^' + c/c^' = -1`

• aa' + cc' = 1

• aa' + cc' = –1

Answer 1

aa' + cc' = –1

Explanation:

Line 1: `(x - b)/a = y/1 = (z - d)/c`   ...(i)

Line 2: `(x - b^')/a = y/1 = (x - d^')/c`   ...(ii)

Given both line perpendicular to each other

Hence, aa' + (1)(1) + cc' = 0

aa' + cc' = –1