The buoyant force on a floating object is a net vertical force acting on it due to pressure. In a static fluid, there will be a balance between the weight of the floating object and the buoyant force. An excellent example of this is an iceberg.Solve e. Thanks!

a.) If G(x, y, z) is a vector-valued function then we define surface and triple integrals of G component-wise. If a is a constant vector, prove that JJa. Gas =a. Gas and Ill, a Gav =a. JJJ Gav b.) The derivative of a vector function is r'(t) = lim [r(t + At) - r(t) ] At-+0 At for all t where the limit exists. Apply this to the quantity fa for scalar f and constant vector a. c.) For the scalar f and the vector F, prove the following identity: V . (fF ) = f ( V . F) +F . Vf d.) Using the results of (a) through (c) above, prove the following: (J, mas = ] ]] vs av e.) The buoyant force on a floating object may be written as B=-JJ pn ds where p is the fluid pressure. The pressure p is related to the density of the fluid p(x, y, z) by a law of hydrostatics: Vp = p(x, y, x)g where g is the acceleration due to gravity. If the weight of the object is W = mg, use the results of parts (a) through (d) above to demonstrate that the object is in static equilibrium