Vector and cartesian equation of line

Find the vector and cartesian equation of a line passes through the points (1,3,2) and origin.

Find the vector and cartesian equation of a line passes through the points (1,3,2) and origin.

Find the vector and cartesian equation of a line through the point (1, – 1, 1) and perpendicular to the lines joining the points (4, 3, 2), (1, -1,0) and (1, 2,-1), (2, 1, 1).

Find the vector and cartesian equations of the line that passes through : the points (1,2,3) and (2,-1,4).

Find the vector and cartesian equation of the line that passes through the points ({:(3,-2,-5):}) and ({:(3,-2,6):})

Find the vector and cartesian equation of the line joining the points (1, -2, 1) and (0, -2, 3).

Find the the vector and cartesian equations of the lines that passes through the origin and (5,-3,3).

Find the vector and cartesian equation of the line through the point (3, -4, -2) and parallel to the vector 9hati+6hatj+2hatk .