Thu November 01, 2012 By: Pramod R

The resultant of two vectors u and v is perpendicular to u and is half of the magnitude of v. Then what is the angle between u and v ? Please explain.

Expert Reply
Thu November 01, 2012
Resultant of 2 vectors 'u' and 'v' is given as
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°
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