# 3. Find the angle between the lines whose direction ratios are a, b, c and b – c, c – a, a – b.

D Divya Prakash Singh

Given direction ratios $a,b,c$  and  $b-c,\ c-a,\ a-b$.

Thus the angle between the lines A is given by;

$A = \left | \frac{a(b-c)+b(c-a)+c(a-b)}{\sqrt{a^2+b^2+c^2}.\sqrt{(b-c)^2+(c-a)^2+(a-b)^2}} \right |$

$\Rightarrow \cos A = 0$

$\Rightarrow A = \cos^{-1}(0) = 90^{\circ}$a

Thus, the angle between the lines is $90^{\circ}$.

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