Q13 of 40 Page 27

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

Let us assume the direction ratios of vectors be (r1,r2,r3) and (r4,r5,r6).


Then,


⇒ (r1,r2,r3) = (a,b,c)


⇒ (r4,r5,r6) = (b–c, c–a, a–b)


We know that the angle between the lines with direction ratios proportional to (a1,b1,c1) and (a2,b2,c2) is given by:


⇒


Using the above formula we calculate the angle between the lines.


Let be the angle between the two lines given in the problem.


⇒


⇒


⇒


⇒


⇒


∴ The angle between two given vectors is .


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