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Question
Find the direction ratios of the line perpendicular to the lines
`(x - 7)/2 = (y + 7)/(-3) = (z - 6)/1` and `(x + 5)/1 = (y + 3)/2 = (z - 6)/(-2)`
Solution
Let L1 and L2 be the given lines with direction ratios 2, – 3, 1 and 1, 2, – 2 respectively.
Let the direction ratios of the line perpendicular to L1 and L2 be a, b, c.
∴ 2a – 3b + c = 0 and a + 2b – 2c = 0
∴ `"a"/|(-3, 1),(2, -2)| = "b"/|(2, 1),(1, -2)| = "c"/|(2, -3),(1, 2)|`
∴ `"a"/(6 - 2) = (-"b")/(-4 - 1) = "c"/(4 +3)`
∴ `"a"/4 = "b"/5 = "c"/7`
∴ The direction ratios of the line are 4, 5, 7.
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