(a) The position vectors of the points X and Y are \(x = (-2i + 5j)\) and \(y = (i - 7j)\) respectively. Find : (i) (3x + 2y) ; (ii) \(|(y - 2x)|\) ; (iii) ...

(a) The position vectors of the points X and Y are \(x = (-2i + 5j)\) and \(y = (i - 7j)\) respectively. Find :

(i) (3x + 2y) ; (ii) \(|(y - 2x)|\) ; (iii) the angle between x and y ; (iv) the unit vector in the direction of \((x + y)\).

(b) A bullet of mass 0.084kg is fired horizontally into a 20 kg block of wood at rest on a smooth floor. If they both move at a velocity of \(0.24 ms^{-1}\) after impact; Calculate, correct to two decimal places, the initial velocity of the bullet.