A vector \vec{a} is turned without a change in its length through a small angle \(d\theta.\) The value of |\Delta \vec{a}| and \Delta a are respectively
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From the (figure) \(\left|\overrightarrow{OA}\right| = a\) and \(\left|\overrightarrow{OB}\right| = a\) .
Also from triangle rule,
\overrightarrow{OB} - \overrightarrow{OA} = \overrightarrow{AB} = \Delta \vec{a}
\(\Rightarrow |\Delta \vec{a}| = AB\)
\(Using angle = \frac{\mathrm{Arc}}{\mathrm{Radius}} \Rightarrow \mathrm{AB} = a \, d\theta\)
So \(|\Delta \vec{a}| = a d \theta\) .
\Delta a means change in the magnitude of vector, i.e., \(\left|\overrightarrow{OB}\right| - \left|\overrightarrow{OA}\right|\)
\(\Rightarrow a - a = 0\)
So \Delta a = 0
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