CBSE Class 11-science Answered

Resultant of 2 vectors 'u' and 'v' is given as
=?{u²+v²+2uvcos?}
Hence
v/2 =?{u²+v²+2uvcos?}
?v² =4{u²+v²+2uvcos?}.....(i)
Angle '?' of resultant with 'u' is given by
tan? =(vsin?)/(u+vcos?)
Since ?=90°
u+vcos?=0 i.e u=?vcos?....(ii)
from (i) and (ii), we get
v² =4{(?vcos?)²+v²+2(?vcos?)vcos?}
? v² =4{v²cos²?)+v²?2v²cos²?
?v² =4v²{1?cos²?}
i.e 1=4?4cos²?}
cos cos²?=3/4 or
cos?=±?3/2 or
Since the resultant is less than 'u' hence angle ?> 90°.
Hence cos?=??3/2 and ?=150°