Let A, B and C is three points on a circle of radius R , if O is the centre of the circle and A O B=45^ , B O C=45^ , then the resultant of O A , O B and O C has magnitude

Step-by-step solution

Given, diagram can be projected on x y- plane as shown here. | O A |=R=| O B |=| O C | O B has projected as A B ^ and O C is projected as B ^ C ^ . Hence, | A B ^ |= | B ^ C ^ |=R and B B ^ C ^ =90^ . Hence, the resultant of O A , O B and O C is O C ^ O C ^ = O B + B C ^ | O C ^ |=| O B |+ | B C ^ | ...(i) In B B^ C^ , using Pythagoras | B C ^ |= R^2+R^2 = 2 R From Eq. (i), we get | O C ^ |=R+ 2 R=( 2 +1) R