Find the vector equation of a line passing through the point with position vector `hati-2hatj-3hatk` and parallel to the line joining the points with position vectors `hati-hatj+4hatk and 2hati+hatj+2hatk`. Also find the cartesian form of the equation.

Find the vector equation of a line passing through a point with position vector 2hati-hatj+hatk and parallel t the line joining the points with position vectors -hati+4hatj+hatk and hati+2hatj+2hatk . Also, find the cartesian equivalent of the equation.

Find the vector equation of a plane passing through the point having position vector 2hati+hatj+hatk and perpendicular to the vector: 4hati-2hatj+3hatk .

Find the equation of the line passing through the point with position vector hati-hatj+2hatk and perpendicular to the plane vecr.(2hati-hatj+3hatk)=5 .

Find the vector equation of a line passing through the point with position vector (2hati-3hatj-5hatk) and perpendicular to the plane vecr*(6hati-3hatj-5hatk)+2=0 . Also, find the point of intersection of this line and the plane.

Find the vector equation of the line which is parallel to the vector 3hati-2hatj+hatk and which passes through the point (1,-2,3).

Show that the three points with position vectors -2hati+3hatj+5hatk , hati+2hatj+3hatk and 7hati-hatk are collinear.

Show that the three points with position vectors 2hati+6hatj+3hatk , hati+2hatj+7hatk and 3hati+10hatj-hatk are collinear.