Prove that the three lines from O with direction cosines `l_1, m_1, n_1: l_2, m_2, n_2: l_3, m_3, n_3` are coplanar, if `l_1(m_2n_3-n_2m_3)+m_1(n_2l_3-l_2n_3)+n_1(l_2m_3-l_3m_2)=0`

l=m=n=1 represent direction cosines of

If A = [[l_(1),m_(1),n_(1)],[l_(2),m_(2),n_(2)],[l_(3),m_(3),n_(3)]] then Find A+I

The angle between the lines whose direction cosines satisfy the equations l+ m +n =0 and l^2= m^2 + n^2 is:

The angle between the lines whose direction cosines satisfy the equation l+m+n=0 and l^(2)=m^(2)+n^(2) is

Simplify (m^2-n^2m)^2+ 2m^3n^2

If veca, vecb and vecc are any three non-coplanar vectors, then prove that points l_(1)veca+ m_(1)vecb+ n_(1)vecc, l_(2)veca+m_(2)vecb+n_(2)vecc, l_(3)veca+m_(3)vecb+ n_(3)vecc, l_(4)veca + m_(4)vecb+ n_(4)vecc are coplanar if |{:(l_(1),, l_(2),,l_(3),,l_(4)),(m_(1),,m_(2),,m_(3),,m_(4)), (n_1,,n_2,, n_3,,n_4),(1,,1,,1,,1):}|=0

The direction cosines l, m, n of two lines are connected by the relation l+m+n=0 and l . m=0 then the angle between them is

Give the possible values of l,m,and s when n=2