Let AP and BQ be two vertical poles at point A and B, respectively. If AP= 16 m, BQ = 22 m and AB=20 m, then find the distance of a point R on AB from the point A such that `RP^2+RQ^2` is minimum.

Let A (1, -1, 2) and B(2, 3, -1) be two points. If a point P divides AB internally in the ratio 2:3, then the position vector of P is

Let P and Q be any two points. Find the coordinates of the point R which divides PQ externally in the ratio 2: 1 and verify that Q is the mid point of P R .

An arch is in the form of a semi-ellipse. It is 8m wide and 2m high at the centre. Find the height of the arch at a point 1.5m from one end.

Consider the points A (2,3) and B (6,5) find the slope of AB

If the points A and B are (1,2,-1) and (2,1,-1) respectively, then vec(AB) is

At a point due to a point charge, the value of electric field intensity and potential are 32 NC^(-1) and 16 JC^(-1) respectively. The magnitude of charge and distance from the charge from the point of observation are.....(a)8.89 × 10 − 10 C, 0.5 m (b)8.89 × 10 − 10 C, 2m (c)2 × 4.6 × 10 − 10 C (d)5 × 4.6 × 10 − 10 C

Consider the point A(2,1,1) and B(4,2,3) .Find the direction cosines of vec(ab)