Show that the lines (x – 5)/7 = (y + 2)/-5 = z/1 and x/1 = y/2 = z/3 are perpendicular to each other.
Answers
Solution :-
Given lines are:
=> (x – 5)/7 = (y + 2)/-5 = z/1 and x/1 = y/2 = z/3
The direction ratios of the given lines are 7, -5, 1 and 1, 2, 3, respectively.
We know that,
Two lines with direction ratios a1, b1, c1 and a2, b2, c2 are perpendicular to each other if a1a2 + b1b2 + c1c2 = 0
Therefore, 7(1) + (-5) (2) + 1 (3)
=> 7 – 10 + 3
=> 0
Hence, the given lines are perpendicular to each other.
Answer: This may help you
Explanation:
The lines which are given:-
(x – 5)/7 = (y + 2)/-5 = z/1 and
x/1 = y/2 =z/3
The direction ratios of the given lines are 7, -5, 1 and 1, 2, 3, respectively.
We know that, Two lines with direction ratios a1, b1, c1 and a2, b2, c2 are perpendicular to each other if a1a2 + b1b2 + c1c2 = 0
Therefore,
=7(1) + (-5) (2) + 1 (3)
=7 – 10 + 3
=0
Hence, the given lines are perpendicular to each other.