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

Find the vector and cartesian equations of the planes : (a) that passes through the point (1, 0, -2) and the normal to the plane is hati+hatj-hatk . (b) that passes through the point (1,4, 6) and the normal vector to the plane is hati-2hatj+hatk .

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 line through the point (5, 2, - 4) and which is parallel to the vector 3hati+2hatj-8hatk. vecr=(5+3lambda)hati+(2+2lambda)hatj+(-4-8lambda)hatk and certesian equations (x-5)/(3)=(y-2)/(2)=(z+4)/(-8)

The cartesian equation of the line passing through (4, 9, 8) and (3, - 2, 1) is ..

Find the vector equations of the plane passing through the points R(2, 5, -3), S(-2,-3, 5) and T(5, 3, -3).

Find the direction cosines of the line passing through the two points (-2, 4, -5) and (1, 2, 3).

Find the vector equation for the line passing through the points (-1, 0, 2) and (3, 4, 6).

Find equation of the circle passes from the points (1, 2) , (3,-4) and (5, -6).