Posted by **manjula** on Tuesday, January 15, 2013 at 2:06am.

if (l1,m1,n1),(l2,m2,n2),(l3,m3,n3) are the direction cosines of three mutual perpendicular lines,show that the line whose direction ratios area l1+l2+l3,m1+m2+m3,n1+n2+n3 make equal angles with them

- analytical geometry -
**drwls**, Tuesday, January 15, 2013 at 3:11am
Because the first three lines are mutually perpendicular, dot products of pairs of lines are zero.

l1*l2+m1*m2+n1*n2 = 0

l2*l3+m2*m3+n2*n3 = 0

l1*l3+m1*m3+n1*n3 = 0

Finally, using the above equations, and another dot product, show that the cosine of the angle between the fourth vector and any of the first three vectors is the same.

- analytical geometry -
**DIPRA**, Monday, August 25, 2014 at 4:52am
listen to me dear.solve these six equations.l1l2+m1m2+n1n2=0,l2l3+m2m3+n2n3=0and l1l3+m1m3+n1n3=0...with these solve theselil2+m1m2+n1n2=l2l3+m2m3+n2n3=l1l3+m1m3+n1n3

## Answer this Question

## Related Questions

- analytical geometry - if (l1,m1,n1),(l2,m2,n2),(l3,m3,n3) are the direction ...
- 3 D - geometry (direction of cosines) - Find the angle between the lines between...
- geometry - A grid has lines at 90-degree angles. There are 12 lines in one ...
- geometry - Martin drew a pair of perpendicular lines and a pair of parallel ...
- Math - a grid has line at 90-degree angles. There are 12 lines in one direction ...
- Geometry - Which of the following statements from Euclidean geometry is also ...
- 4th grade - Geometry, Isoseles right triangle. Line segments MN and NO are...
- Geometry - Which statement from Euclidean geometry is also true in spherical ...
- maths geometry - Find and write down a proof that the product of the gradients ...
- Algebra - Which of the following statements from Euclidean geometry is also true...