Homework Help: analytical geometry

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.

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