Question

The resultant of two vectors ū and v vector is perpendicular to vector ū and its magnitude is equal to
Half of the magnitude of vector v. Find the angle between ū and v.
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Answer 1

Answer:

Explanation:Resultant of 2 vectors 'u' and 'v' is given as

=?{u�+v�+2uvcos?}

Hence  

v/2 =?{u�+v�+2uvcos?}

?v� =4{u�+v�+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

v� =4{(?vcos?)�+v�+2(?vcos?)vcos?}

? v� =4{v�cos�?)+v�?2v�cos�?

?v� =4v�{1?cos�?}

i.e 1=4?4cos�?}

cos cos�?=3/4 or  

cos?=�?3/2 or  

Since the resultant is less than 'u' hence angle ?> 90�.  

Hence cos?=??3/2 and ?=150�