If the coordinates of the points $A, B, C, D$ are $(2, 3, -1), (3, 5, -3), (1, 2, 3)$ and $(3, 5, 7)$ respectively,then the projection of $AB$ on $CD$ is

If the direction cosines of two lines are $(\frac{2}{3}, \frac{2}{3}, \frac{1}{3})$ and $(\frac{5}{13}, \frac{12}{13}, 0)$,then identify the direction ratios of a line which is bisecting one of the angles between them.

The direction cosines of three lines passing through the origin are $(l_1, m_1, n_1)$,$(l_2, m_2, n_2)$,and $(l_3, m_3, n_3)$. The lines will be coplanar if

What do the three lines with direction ratios $(1, 1, 2)$,$(\sqrt{3}-1, -\sqrt{3}-1, 4)$,and $(-\sqrt{3}-1, \sqrt{3}-1, 4)$ represent?

If the direction ratios of a line are $1, -3, 2$,then the direction cosines of the line are

The angle between the lines whose direction cosines $(\ell, m, n)$ satisfy the equations $\ell+m+n=0$ and $\ell^2+m^2-n^2=0$ is: