Find the position vector of a point R which divides the line joining the points `P(hati+2hatj-2hatk)` and `Q(hati+2hatj+2hatk)` internally in the ratio 1:2.

Find the position vector of a point R which divides the line joining the points P(hati+2hatj-hatk ) and Q(hati+2hatj+2hatk) internally in the ratio 2:1.

Find the angle between the vectors hati-2hatj+3hatk and 3hati - 2hatj + hatk

If p=7hati-2hatj+3hatk and q=3hati+hatj+5hatk , then find the magnitude of p-2q.

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.