Find the equation of the line in vector and in cartesian form that passes through the point with position vector `2hati-hatj+4hatk` and is in the direction `hati + 2hatj - hatk`

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 .

Write the projection of the vector 7hati+hatj+4hatk on the vector 2hati+6hatj+3hatk .

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 projection of the vector hati+3hatj+7hatk on the vector 2hati-3hatj+6hatk .

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 the plane passing through three points with position vectors hati+hatj-2hatk, 2hati-hatj+hatk and hati+2hatj+hatk . Also find the co-ordinates of the point of intersection of this plane and the line vecr=3hati-hatj-hatk+lambda(2hati-2hatj+hatk) .

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 equation in vector anf cartesian form of the line passing through the point : (2,-1,3) and perpendicular to the lines vecr= (hati+hatj-hatk)+lambda(2hati-2hatj+hatk) and vecr= (2hati-hatj-3hatk)+mu(hati+2hatj+2hatk) .

Find the distance of the point whose position vector is 2hati+hatj-hatk from the plane vecr.(hati-2hatj+4hatk)=9 .