The position vectors of P, Q and R with respect to the origin are (4i-5j), (i+3j) and (-5i+2j) respectively. If PQRM is a parallelogram, find:

(a) the coordinates of M;

(b) the acute angle between \(\overline{PM}\) and \(\overline{PQ}\), correct to the nearest degree.

(a) A girl threw a stone horizontally with a velocity of 30m/s from the top of a cliff 50m high. How far from the foot of the cliff does the stone strike the ground? [Take g= 10m/s\(^2\)

(b)

(b) A body A, of mass 2kg is held in equilibrium by means of two strings AP and AR. AP is inclined at 56° to the upward vertical and AR is horizontal.

Find the tensions T\(_1\), and T\(_2\), in the strings [Take g= 10ms\(^2\)]

A binary operation ∆ is defined on the set of real numbers R, by x∆y = \(\sqrt{x+y - \frac{xy}{4}}\), where x, yER. Find the value of 4∆3

(\(\frac{3√6}{√5} + \frac{√54}{3√5}\))\(^{-1}\)

If \(log_{10}(3x+1) + log_{10}4 = log_{10}(9x+2)\), find the value of x