Question

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

Answer 1

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

$⇒ \cosθ = 0$

$⇒ θ = \cos ^{ - 1}$

$θ = 90°$

$angle \: between \: line \: is \: 90°$