Show that the three lines drawn from the origin with direction cosines proportional to 1,-1,1,2,-3,0 and 1,0,3 are coplanar

Three lines are drawn from the origin O with direction ratio proportional to 1,-1,1,2,-3,0 and 1,0,3. The three lines are

Prove that three lines drawn from origin with direction cosines proportional to (1,-1,1),(2,-3,0),(1,0,3) lie on one plane .

Prove that the three lines drown from origin 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_1,n_1],[l_2,m_2,n_2],[l_3,m_3,n_3]]=0.

The acute angle between the lines whose direction cosines are proportional to 3,-1,2 and 2,1,-3 is

Find the direction cosines of the line which is perpendicular to the lines with direction cosines proportional to 1, -2, -2 and 0, 2, 1

Find the direction cosines of the line which is perpendicular to the lines with direction cosines proportional to 1, -2, -2 and 0, 2, 1

Find the direction cosines of the line which is perpendicular to the lines with direction cosines proportional to 1, -2, -2 and 0, 2, 1

There are three straight lines through the origin with direction cosines proportional to (1,2,2), (2,3,6) (3,4,12), Find the direction cosines of a a line equally inclined to the given lines.