Question

Find the direction ratios of a vector perpendicular to the two lines whose direction ratios are 1, 3, 2 and –1, 1, 2

Answer 1

Let L₁ and L₂ be the two lines with direction ratios 1, 3, 2 and –1, 1, 2 respectively.

Let the direction ratios of the vector perpendicular to L₁ and L₂ be a, b, c.

∴ a + 3b + 2c = 0

and −a + b + 2c = 0

∴ `"a"/|(3, 2),(1, 2)| = (-"b")/|(1, 2),(-1, 2)| = "c"/|(1, 3),(-1, 1)|`

∴ `"a"/(6 - 2) = (-"b")/(2 + 2) = "c"/(1 + 3)`

∴ `"a"/4 = (-"b")/4 = "c"/4`

∴ The direction ratios of the vector are 4, – 4, 4.