Let AP and BQ be two vertical poles at points 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.

A man goes 18 m due east and then 24 m due north. Find the distance of his current position from the starting point ?

A man goes 10 m due east and then 24 m due north. Find the distance of his current position from the starting point ?

If A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P on AB such that AP = (3)/(7) AB.

The angle of elevation of the top of a vertical tower standing on a horizontal plane is observed to be 45^(@) from a point A on the plane. Let B be the point 30 m vertically above the point A. If the angle of elevation of the top of the tower from B be 30^(@) , then the distance then the distance (in m) of the foot of the tower from the point A is

ABCD is a trapezium in which AB||DC and P,Q are points on AD and BC respectively, such that PQ||DC if PD=18 cm , BQ= 35 cm and QC= 15 cm, find AD.

Two point charges +q and -q are placed at points A and B respectively separated by a samll distance. The electric field intensity at the midpoint O of AB :

Find the distance of the z-axis from the image of the point M(2-3,3) in the plane x-2y-z+1=0.

Find the coordinates of points Q and R on medians BE and CF respectively such that BQ:CF =2:1 and CR:RF =2:1​