Show that the lines are perpendicular to each other.

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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