Find the vector and Cartesiasn equation of the line that passes through the origin and (5,-2,3).

Find the vector and the cartesian equations of the lines that passes through the origin and (5, 2, 3) .

Find the vector and the cartesian equations of the line that passes through the points (3, 2, 5), (3, 2, 6) .

Find the vector and cartesian equations of the plane which passes through the point (5, 2, 4) and perpendicular to the line with direction ratios (2, 3, 1) .

Find the vector and the Cartesian equations of the plane passing through the point (1,2,3) and perpendicular to the line with direction ratio 2,3,-4.

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

Find the equation of a line passing through the points (3,5) and (-2, 1).

Find the differential equation of the family of lines passing through the origin.

Find the cartesian equation of the line which passes through the point (-2,4,-5) and parallel and line are (3,5,6) .

Find the equation of a line passing through the points (2,5) and (-3,1) .

Find the equation of a circle passes through the origin and whose centre is (-2,5).