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

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

Lines OA and OB are drawn from O with directioncosines proportional to (1,-2,-1) and (3,-2,3) respectively. The direction ratios of the normal to the planes AOB are (A) (4,3,2) (B) (4,-3,-2) (C) (-4,3,-2) (D) (4,3,-2)

Find the direction cosines of the line joining the points (1,-1,0) and (2, 1, 3).

An equation of the plane passing through the origin and containing the lines whose direction cosinesare proportional to 1, -2,2 and 2, 3, -1 is

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 direction cosines of the line drawn from P(-5,3,1) to Q(1,5,-2) is

If direction cosines of a line are (1/a, 1/a, 1/a) then

The direction cosines of the line passing through P(2,3,-1) and the origin are

Direction ratios of the line are 2, 1, -3 . Find the direction cosines.