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