If , and , find a unit vector parallel to the vector .

Find the value of x for which is a unit vector.

Find a vector of magnitude 5 units, and parallel to the resultant of the vectors and

Show that the points A(1, – 2, – 8), B(5, 0, –2) and C(11, 3, 7) are collinear, and find the ratio in which B divides AC.

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