Vector Calculus Answers

Find a . b and a X b if a=i+2j+k and |b| = 3 acting along c = i + j + k.

If A, B, C are any three vectors then show that AX(B+C) = AXB+AXC.

find the point of intersection of planes in vector form ('.' refers to dot product) r.a=1,r.b=1 ,r.c=1 where a,b,c are non co-planner vectors.

Evaluate the surface integral double integral s F * dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.

F(x,y,z) = xyi + 12x^2j + yzk
S is the surface z = xe^y, 0 less than or equal to x less than or equal to 1, 0 less than or equal to y less than or equal to 4, with upward orientation.