Q. 134.9( 21 Votes )

Show that the lines are perpendicular to each other.

Answer :

We know that

Two lines with direction ratios a1, b1, c1 and a2, b2, c2 are perpendicular if the angle between them is θ = 90°, i.e. a1a2 + b1b2 + c1c2 = 0


Also, here the direction ratios are:


a1 = 7, b1 = -5, c1 = 1 and a2 = 1, b2 = 2, c2 = 3


Now, Consider


a1a2 + b1b2 + c1c2 = 7 × 1 + (-5) × 2 + 1 × 3 = 7 -10 + 3 = - 3 + 3 = 0


The two lines are perpendicular to each other.


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