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 angle between the lines whose direction cosines are l, m, n and m-n, n-l, l-m is......

Show that the straight lines whose direction cosines are given by 2l + 2m - n = 0 and mn + nl + Im = 0 are at right angles.

The angle between the lines whose direction cosines are given by l + m + n = 0 and l^2 = m^2 + n^2 is .....

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 lines whose direction cosines are given by the equation l + m + n = 0 and l^2 + m^2 - n^2 = 0.

What are the possible values of l for an electron with n=3 ?

Calculate the vlue of (n+l) for 3d

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

The position vectors of points of intersection of three planes rcdotn_1=q_1, rcdotn_2=q_2, rcdotn_3=q_3, where n_1, n_2 and n_3 are non coplanar vectors, is

If (l_1, m_1, n_1), (l_2, m_2, n_2)" and "(l_3, m_3, n_3) are the direction cosines of three mutually perpendicular lines, prove that the line whose direction cosines are proportional to (l_1+l_2+l_3,m_1+m_2+m_3,n_1+n_2+n_3) makes equal angles with them,