VC1.2

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Given, r=3i-6t^{2}j+4tk

Since i,j,k are constant vectors, {\frac  {di}{dt}}={\frac  {dj}{dt}}={\frac  {dk}{dt}}=0

Therefore, from the given {\frac  {dr}{dt}}={\frac  {d}{dt}}(3)i-{\frac  {d}{dt}}(6t^{2})j+{\frac  {d}{dt}}(4t)k=-12tj+4k

From the above, {\frac  {d^{2}r}{dt^{2}}}={\frac  {d}{dt}}[{\frac  {dr}{dt}}]=-{\frac  {d}{dt}}(12t)j+{\frac  {d}{dt}}(4)k=-12j

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