Question

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

Answer 1

The angle Q between the lines with direction cosines, a,b,c and b-c, c-a, a-b, is given by,

cosQ=|$\frac{a(b-c)+b(c-a)+c(a-b)}{\sqrt{a^2+b^2+c^2}+\sqrt{(b-c)^2+(c-a)^2+(a-b)^2}}$|

⇒cosQ=0

⇒Q=cos-1=0

⇒Q=90°

Thus, the angle between the lines is 90°.