Q.

Let 3i^+j^,i^+3j^ and βi^+(1-β)j^ respectively be the position vectors of the points A, B and C with respect to the origin O. If the distance of C from the bisector of the acute angle between OA and OB is 32, then the sum of all  possible values of β is

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Detailed Solution

Since, the angle bisector of acute angle between OA and OB would be y=x Since, the distance of Cβ,1-β from the bisector y=x is 32,⇒β-(1-β)2=32 ⇒2β=±3+1 ⇒β=2 or β=-1 Hence, the sum of all possible value of β=2+(-1)=1
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