The divergence of the vector field $$\left( {x - y} \right)\widehat i + \left( {y - x} \right)\widehat j + \left( {x + y + z} \right)\widehat k$$ is

Let $$\,\,f = {y^x}.$$ What is $$\,\,{{{\partial ^2}f} \over {\partial x\partial y}}\,\,$$ at $$x=2,$$ $$y=1$$?

A circular disk of radius $$'R'$$ rolls without slipping at a velocity $$v$$. The magnitude of the velocity at point $$'P'$$ (see figure) is

Consider a truss $$PQR$$ loaded at $$P$$ with a force $$F$$ as shown in the figure. The tension in the member $$QR$$ is