Find the divergence and curl of the vector field V=(x2−y2)i^+2xyj^+(y2−xy)k^ If F=(x+y+1)i^+j^−(x+y)k^, show that F.cu
Posted: Thu Jul 14, 2022 4:21 pm
Find the divergence and curl of the vector field V=(x2−y2)i^+2xyj^+(y2−xy)k^ If F=(x+y+1)i^+j^−(x+y)k^, show that F.curl F=0. Find divF and curl F where F=grad(x3+y3+z3−3xyz). Find out values of a,b,c for which v=(x+y+az)i^+(bx+3y−z)j^+(3x+cy+z)k^ is irrotational. Determine the constants a,b,c, so that F=(x+2y+az)i^+(bx−3y−z)j^+(4x+cy+2z)k^ is irrotational. Hence find the scalar potential ϕ such that F=gradϕ.