given A and B are postion vectors a=2i-2j-k and b=3i+4k
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The unit vector OA= a/|a|= (2/3)i - (2/3)j - (1/3)k
Unit vector OB=b/|b|=(3/5)i+(4/5)k
A vector bisecting the angle AOB is the sum of these vectors
V=(2/3+3/5)i -(2/3)j +(4/5 - 1/3)k =(19/15)i - (2/3)j + (7/15)k = (1/15)[19i-10j+7k)
This has magnitude sqrt(19/15)^2 + (2/3)^2+(7/15)^2) =√(34/15)
Required vector is V/√(34/15) =√(15/34)[(1/15)[19i-10j+7k)
√(15/34) (1/15) =√(510)/510 giving the correct answer.
Unit vector OB=b/|b|=(3/5)i+(4/5)k
A vector bisecting the angle AOB is the sum of these vectors
V=(2/3+3/5)i -(2/3)j +(4/5 - 1/3)k =(19/15)i - (2/3)j + (7/15)k = (1/15)[19i-10j+7k)
This has magnitude sqrt(19/15)^2 + (2/3)^2+(7/15)^2) =√(34/15)
Required vector is V/√(34/15) =√(15/34)[(1/15)[19i-10j+7k)
√(15/34) (1/15) =√(510)/510 giving the correct answer.