Motion in a plane

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Question

The rectangular components of a vector lying in xy plane are (n+1) and 1. If coordinate system is turned by 60^o , they are n & 3 respectively the value of ‘n’

Moderate

Solution

Rotation of co-ordinate system does not change the vector.
Hence
$\large \sqrt{(n+1)^2+1^2}=\sqrt{n^2+3^2}$
⇒ n²+2n+1+1 = n² +9
⇒ 2n = 7 ⇒ n = 3.5

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