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Question
Show that the lines `(x-5)/7 = (y + 2)/(-5) = z/1` and `x/1 = y/2 = z/3` are perpendicular to each other.
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Solution
The ratio of the given slave
a1, b1, c1 = 7, −5, 1 and a2, b2, c2 = 1, 2, 3
∵ The lines are perpendicular to each other.
∴ a1a2 + b1b2 + c1c2 = 0
ya 7 × 1 + (−5) × (2) + (1) × 3 = 0
and 7 − 10 + 3 = 0
or 0 = 0, which is true
Therefore, the lines are perpendicular to each other.
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