Add: `3m^(2)n + 5mn^(2) - 7mn` and `2m^(2)n - mn^(2) + mn`

Which polynomial should be subtracted from 3m^2 n +5mn^2 -2m^2 n^2 to get the polynomial -m^2 n +7mn^2 +4m^2 n^2 .

If l , m, n are the direction cosines of a line, then: a) l^(2)+m^(2)+n^(2)=1 b) l^(2)+m^(2)+n^(2)=0 c) l+m+n=1 d) l+m+n=0

If m and n are two distinct numbers such that m >n, then prove that m^2-n^2 ,2mn and m^2+n^2 is a Pythagorean triplet.

If the direction cosines of two lines are l_(1), m_(1), n_(1) and l_(2), m_(2), n_(2) , then find the direction cosine of a line perpendicular to these lines. a) l_(1)+l_(2),m_(1)+m_(2),n_(1)+n_(2) b) l_(1)-l_(2),m_(1)-m_(2),n_(1)-n_(2) c) m_(1)n_(2)-m_(2)n_(1),n_(1)l_(2)-n_(2)l_(1),l_(1)m_(2)-l_(2)m_(1) d) l_(1)+2l_(2),m_(1)+2m_(2),n_(1)+2n_(2)