Question

Given lines are \[ x = my + n, \, z = py + q \] and \[ x = m'y + n', \, z = p'y + q' \] Above equations can be rewritten as \[ x - n' = p', \quad m = 1, \, p = 1 \] Lines will be perpendicular if

• A. \( mm' + pp' = 1 \)
• B. \( \frac{m}{m'} + \frac{p}{p'} = 1 \)
• C. \( \frac{m}{m'} = 1 \)
• D. \( mm' + pp' = -1 \)

Hint:

For two lines to be perpendicular, their slope products should satisfy the condition \( mm' + pp' = 1 \).

Answer 1

The Correct Option is A

For two lines to be perpendicular, the condition \( mm' + pp' = 1 \) must hold, which follows from the geometric properties of line slopes.