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If \( \vec{A}=t^{2} \hat{\imath}-t \hat{\jmath}+(2 t+1) \hat{k} \) and \( \vec{B}=(2 t-3) \hat{\imath}+\hat{\jmath}-t \hat{k} \) find (i) \( \frac{d}{d t}(\vec{A} . \vec{B}) \) (ii) \( \frac{d}{d t}(\vec{A} \times \vec{B}) \)

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If \( \vec{A}=t^{2} \hat{\imath}-t \hat{\jmath}+(2 t+1) \hat{k} \) and \( \vec{B}=(2 t-3) \hat{\imath}+\hat{\jmath}-t \hat{k} \) find (i) \( \frac{d}{d t}(\vec{A} . \vec{B}) \) (ii) \( \frac{d}{d t}(\vec{A} \times \vec{B}) \)
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