For any two vectors and , show that:

If , are given vectors, then find a vector satisfying the equations and .

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are and externally in the ratio 1:2. Also, show that p is the mid-point of the line segment RQ.

If are three mutually perpendicular vectors of equal magnitude, prove that is equally inclined with vectors and . Also, find the angle.

If four points A, B, C and D with position vectors and respectively are coplanar, then find the value of x.