vector calculus for solid mechanics

Problem 1: Give the following two vectors in Euclidean orthonormal coordinate system If u is defined by points Q to P and v is defined by points N to M. Determine the expression for vector u and vector v Determine the dyadic product of: udv and v Qu M (2, 0, 3) P (1, 0, 2) N (0, 1, 0.5) Q (0.5, 1.5, 0) Problem 2: If u = xu and v =ox v, Show that - (u x v) = w x (ux v) Hint: start form taking the derivative of (u x v) in symbolic form Problem 3: For two arbitrary vector a and b, show that; (a x b) . (axb) + (a.b)2 = (ab)2 Problem 4: If 0 = x+ 5x2 - 4x2x3 and A; [2x1x2 , 4x3x2 , 3x2x3 |7, determine the followings: grad 0 grad (div A) div A div (grad O) Curl A curl (grad O)