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

What is the cosine of the angle which the vector makes with y-axis?

On a multiple choice examination with three possible answers (out of which only one is correct) for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

Find the Cartesian equation of the plane passing through the points A(0, 0, 0) and B(3, - 1, 2) and parallel to the line

Using elementary row operations, find the inverse of the following matrix :