Question

# If l1,m1,n1 and l2,m2,n2 be the DC's of two concurrent lines, the direction cosines of the line bisecting the angles between them are proportional to

A
l1l2,m1m2,n1,n2
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B
l1m2,l1n2,l1n3
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C
l1+l2,m1+m2,n1+n2
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D
None of these
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Solution

## The correct option is D l1+l2,m1+m2,n1+n2Let direction cosines of OA=(l1,m1,n1) and direction cosines of OB=(l2,m2,n2).Taking two points on l and m such that OA=OB=rLet C be the mid-point of AB. Then, OC is the bisector of the angle AOB.Now, coordinates of A are (l1r,m1r,n1r) and coordinates of B are (l2r,m2r,n2r).∴ the coordinates of C are(l1+l2)r2,(m1+m2)r2,(n1+n2)r2.Hence, the direction cosines of OC are proportional to l1+l2,m1+m2 and n1+n2.

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