Q. 134.9( 21 Votes )

# Show that the lines are perpendicular to each other.

Answer :

We know that

Two lines with direction ratios a_{1}, b_{1}, c_{1} and a_{2}, b_{2}, c_{2} are perpendicular if the angle between them is θ = 90°, i.e. a_{1}a_{2} + b_{1}b_{2} + c_{1}c_{2} = 0

Also, here the direction ratios are:

a_{1} = 7, b_{1} = -5, c_{1} = 1 and a_{2} = 1, b_{2} = 2, c_{2} = 3

Now, Consider

a_{1}a_{2} + b_{1}b_{2} + c_{1}c_{2} = 7 × 1 + (-5) × 2 + 1 × 3 = 7 -10 + 3 = - 3 + 3 = 0

∴ The two lines are perpendicular to each other.

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