If l1,m1,n1,l2,m2,n2 and l3,m3,n3 are the direction cosines of three mutually perpendicular lines,then prove that the line whose direction cosines are proportional to l1+l2+l3,m1+m2+m3 and n1+n2+n3 makes equal angles with them.

If l1,m1,n1,l2,m2,n2 and l3,m3,n3 are the direction cosines of three m

1.	If l1,m1,n1,l2,m2,n2 and l3,m3,n3 are the direction cosines of three mutually perpendicular lines,then prove that the line whose direction cosines are proportional to l1+l2+l3,m1+m2+m3 and n1+n2+n3 makes equal angles with them.
Answer» 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.