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 A = i 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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