Find the angle between the lines whose direction ratios are a, b, c and `b - c , c - a , a - b`.

Explanation

The direction ratios of given lines are `(a,b,c)` and `(b-c,c-a,a-b)`
Let `theta` be the acute angle between the two lines, then
`cos theta =|(a(b-c)+b(c-a)+c(a-b))/(sqrt(a^(2)+b^(2)+c^(2))sqrt((b-c)^(2)+(c-a)^(2)+(a-b)^(2)))|`
`= |(ab-ac+bc-ab+ca-bc)/(sqrt(a^(2)+b^(2)+c^(2))+sqrt((b-c)^(2)+(c-a)^(2)+(a-b)^(2)))|=0`
`rArr cos theta = 0 rArr theta = (pi)/(2) = 90^(@)`.
Therefore, angle between two lines is `90^(@)`.