If l1,m1,n1 ; l2,m2,n2 be the direction cosines of two concurrent lines, then direction cosines of the line bisecting the angles between them are proportional to ?

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Q. If

l_{1}, m_{1}, n_{1}

and

l_{2}, m_{2}, n_{2}

be the DC's of two concurrent lines, the direction cosines of the line bisecting the angles between them are proportional to

Q. Assertion :The direction cosines of one of the angular bisectors of two intersecting lines having direction cosines as

l_{1}, m_{1}, n_{1}

and

l_{2}, m_{2}, n_{2}

are proportional to

l_{1} + l_{2}, m_{1} + m_{2}, n_{1} + n_{2}

. Reason: The angle between the two intersecting lines having direction cosines as

l_{1}, m_{1}, n_{1}

and

l_{2}, m_{2}, n_{2}

is given by

cos θ = l_{1} l_{2} + m_{1} m_{2} + n_{1} n_{2}

If $l_{1}, m_{1}, n_{1}, l_{2}, m_{2}, n_{2} a n d l_{3}, m_{3}, n_{3}$ are the direction cosines of three mutually perpendicular lines,then prove that the line whose direction cosines are proportional to $l_{1} + l_{2} + l_{3}, m_{1} + m_{2} + m_{3} a n d n_{1} + n_{2} + n_{3}$ makes equal angles with them.

Q. The direction cosines of the lines bisecting the internal angle

θ

between the lines whose direction cosines are

l_{1}, m_{1}, n_{1}

and

l_{2}, m_{2}, n_{2}

are

Q. The direction cosines of the lines bisecting the angle between the lines whose direction cosines are

l_{1}, m_{1}, n_{1}

and

l_{2}, m_{2}, n_{2}

and the angle between these lines is

θ

, are

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