If `l_1,m_1,n_1andl_2,m_2,n_2` are the direction cosines of two mutually perpendicular lines show that the d.cs. Of the line perpendicular to both of them are `m_1n_2-n_1m_2,n_1l_2-l_1n_2,l_1m_2-m_1l_2`

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 them are m_(1)n_(2) - n_(1)m_(2), n_(1)l_(2) - l_(1)n_(2), l_(1)m_(2) - m_(1)l_(2)

If l,m,n be d.cs, of a line ,then the line is perpendicular to the plane x-3y+2z+1=0 if ______.

Prove that the two lines whose direction cosines are connected by the equations l+2m+3n=0, 3lm-4ln+mn=0 are perpendicular to each other.

Show that the coefficient of a^m and a^n in expansion of (1+a)^(m+n) are equal.

Find the angle between the lines whose dcs. L, m, n are connected by the relation, 3l+m+5n=0 and 6mn-2nl+5lm=0