Q19 of 136 Page 28

Show that the lines and are perpendicular to each other.

The Cartesian equation of the lines are and and we need to find that weather the lines are perpendicular or not, so we will use the dot product equation, as we know the direction ratios of both the lines.

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


Hence the given lines are perpendicular because,


cos θ = 0


θ =


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