. Use the rule of differentiation of the scalar product, to evaluate (u v) for the following vector fields: u = e¹¹ i + 4t² j + 1 k. and a) Calculate the time derivatives of u and v. Represent your answers in the form i+ j+ u= and v = i+ j+ k v = 5i+ sin(3t)j + cos(6t) k. k. b) Now calculate the time derivative of scalar product of u and v: d (u v)=

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Q: F(t) = (Cos(Tt), - 1), G(1) = (1, 1, – 1), G'(1) = (2, 3, 2) , Ĝ"(1) = (0, 1, 0) . (F.G) 1) (Gxở)…

A: Given :- F →t =  cos πt , e2t-1 , t2 - 1  , G →1 =  1 , 1 , -1G' →1 =  2, 3, 2G'' →1 =  0 , 1 , 0…

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