Question 12.13: If a = 3ti -t² j and b = 2t² i + 3j, verify (a) d/dt (a.b) ......

If \mathbf{a}=3 t \mathbf{i}-t^2 \mathbf{j} \text { and } \mathbf{b}=2 t^2 \mathbf{i}+3 \mathbf{j}, verify

(a) \frac{\mathrm{d}}{\mathrm{d} t}(\mathbf{a} \cdot \mathbf{b})=\mathbf{a} \cdot \frac{\mathrm{d} \mathbf{b}}{\mathrm{d} t}+\frac{\mathrm{d} \mathbf{a}}{\mathrm{d} t} \cdot \mathbf{b}           (b) \frac{\mathrm{d}}{\mathrm{d} t}(\mathbf{a} \times \mathbf{b})=\mathbf{a} \times \frac{\mathrm{d} \mathbf{b}}{\mathrm{d} t}+\frac{\mathrm{d} \mathbf{a}}{\mathrm{d} t} \times \mathbf{b}