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`

The direction ratios of the bisector of the angle between the lines whose direction cosines are l_1,m_1,n_1 and l_2,m_2,n_2 are (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) l_1m_2-l_2m_1,m_1n_2-m_2n_1,n_1l_2-n_2l_1 (D) l_1m_2+l_2m_1,m_1n_2+m_2n_1,n_1l_2+n_2l_1

If three mutually perpendicular lines have direction cosines (l_1,m_1,n_1),(l_2,m_2,n_2) and (l_3 ,m_3, n_3) , then the line having direction ratio l_1+l_2+l_3,m_1+ m_2+m_3, and n_1 + n_2 + n_3 , make an angle of

Two lines with direction cosines l_1,m_1,n_1 and l_2,m_2,n_2 are at righat angles iff (A) l_1l_2+m_1m_2+n_1n_2=0 (B) l_1=l_2,m_1=m_2,n_1=n_2 (C) l_1/l_2=m_1/m_2=n_1/n_2 (D) l_1l_2=m_1m_2=n_1n_2

Statement 1: The direction cosines of one of the angular bisectors of two intersecting line having direction cosines as l_1,m_1, n_1a n dl_2, m_2, n_2 are proportional to l_1+l_2,m_1+m_2, n_1+n_2dot Statement 2: The angle between the two intersection lines having direction cosines as l_1,m_1, n_1a n dl_2, m_2, n_2 is given by costheta=l_1l_2+m_1m_2+n_1n_2dot

Find the angle between the line whose direction cosines are given by l+m+n=0a n d2l^2+2m^2-n^2-0.

Find the angle between the line whose direction cosines are given by l+m+n=0a n d2l^2+2m^2-n^2-0.

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 are given by the equatios l^2+m^2-n^2=0, m+n+l=0 is

If vec aa n d vec b are two non-collinear vectors, show that points l_1 vec a+m_1 vec b ,l_2 vec a+m_2 vec b and l_3 vec a+m_3 vec b are collinear if |l_1 l_2 l_3 m_1m_2m_3 1 1 1|=0.

Find the angle between the lines whose direction cosines are given by the equations 3l+m+5n=0,6m n-2n l+5lm=0