Find the equation of the line parallel to `hati-2hatj-3hatk` and passing through the point (5,-1,4)`

Find the vector equation of a line parallel to the vector 2hati-hatj+2hatk and passing through a point A with position vector 3hati+hatj-hatk .

Find the equation of the line (vector and Cartesian both) which is parallel to the vector 2hati-hatj+3hatk and which passes through the point (5,-2,4)

Find the vector equation of the line which is parallel to the vector 3hati-2hatj+6hatk and which passes through the point (1,-2,3) .

Find the vector equation of the line which is parallel to the vector 3hati-2hatj+6hatk and which passes through the point (1,-2,3) .

Find the vector equation of the line which is parallel to the vector 3hati-2hatj+6hatk and which passes through the point (1,-2,3) .

Find the equation of the line passing through point 2hati-hatj+3hatk and parallel to vector hati+hatj-2hatk in vector form as well as Cartesian form.

Find the equation of the plane through the point hati+4hatj-2hatk and perpendicular to the line of intersection of the planes vecr.(hati+hatj+hatk)=10 and vecr.(2hati-hatj+3hatk)=18.

Find the equation of the plane passing through the point hati-hatj+hatk and perpendicular to the vectro 3hati-hatj-2hatk and show that the point 2hati+4hatj lies on the plane.

Find the equation of a line passing through the point (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 equation of a line passes through the point hati+hatj+5hatk and parallel to line joining the points (2,-4,1) and (0,1,3) .