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CBSE Class 11-science Answered

if the sum of two unit vectors is a unit vector,then calculate magnitude of their differnce.

Asked by ABHILASHA | 05 Aug, 2019, 09:03: PM
Expert Answer
(Vectors are typed as Bold. i, j are unit vectors along x and y direction respectively )
 
Let Ai   and  B = a i + b j are unit vecors.
 
Hence (a2 +b2 )  = 1 ......................(1)
 
A+B = (a+1) i + b j
 
if (A+B) is unt vector then  (a+1)2 + b2 =1  ...................(2)
 
By solving eqn.(1) and (2), we get,  a = -1/2  and  b = √3/2
 
Then A - B = (3/2) i - (√3/2) j  ;  magnitude of (A - B) = [ (9/4) + (3/4) ]1/2  = √3
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