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Question -

Show that the lines
   are perpendicular to each other.



Answer -

The equations of thegiven lines are

Two lines withdirection ratios is given as

a1a2 +b1b2 + c1c2 = 0

So the directionratios of the given lines are 7, -5, 1 and 1, 2, 3

i.e., a1 =7, b1 = -5, c1 = 1 and

a2 =1, b2 = 2, c2 = 3

Now, Considering

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

= 7 -10 + 3

= – 3 + 3

= 0

 The two linesare perpendicular to each other.

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