Let `l_1,m_1,n_1; l_2,m_2,n_2` and `l_3,m_3,n_3` be the direction cosines of three mutually perpendicular lines. Show that the direction ratios of the line which makes equal angles with each of them are `(l_1+l_2+l_3),(m_1+m_2+m_3),(n_1+n_2+n_3)`

If l_1,""""m_1,""""n_1 and l_2,""""m_2,""""n_2 are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are m_1n_2-m_2n_1, n_1l_2-n_2l_1, l_1m_2-l_2m_1 .

l = m = n = 1 are the direction Cosines of

If "l"_1,("\ m")_1,("\ n")_1("\ and\ l")_2,("\ m")_2,"n"_2 be the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of them are ("m"_1("\ n")_2-"m"_2"n"_1),"\ "("n"_1"l"_2-"n"_2"l"_1),"\ "("l"_1"m"_2-"l"_2"m"_1)dot

If l_(1), m_(1), n_(1) and l_(2),m_(2),n_(2) are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are m_(1)n_(2)-m_(2)n_(1),n_(1)l_(2)-n_(2)l_(1),l_(1)m_(2)-l_(2)m_(1) .

(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)),(l_(3),m_(3),n_(3)) are the direction cosines of three mutually perpendicular lines. If the line, whose direction ratios are l_(1)+l_(2)+l_(3),m_(1)+m_(2)+m_(3),n_(1)+n_(2)+n_(3) , makes angle theta with any of these three lines, then cos theta is equal to

If 11,m1,n1;12,m2,n2;13,m3,n3 are direction cosines of 3 mutually perpendicular lines then prove that the line whose directional cosines are perpendicular to 11+12+13 ,m1+m2+m3,n1+n2+n3 makes equal angles with them

If l_(1),m_(1),n_(2);l_(2),m_(2),n_(2), be the direction cosines of two concurrent lines,then direction cosines of the line bisecting the angles between them are proportional to