If $$A$$ $$(0,4,3),$$ $$B(0,0,0)$$ and $$C(3,0,4)$$ are there points defined in $$x, y, z$$ coordinate system, then which one of the following vectors is perpendicular to both the vectors $$\overrightarrow {AB} $$ and $$\overrightarrow {BC} $$.

The eigen values of the following matrix $$\left[ {\matrix{ {10} & { - 4} \cr {18} & { - 12} \cr } } \right]$$ are

Water is flowing through a horizontal pipe of constant diameter and the flow is laminar. If the diameter of the pipe is increased by $$50\% $$ keeping the volume flow rate constant, then the pressure drop in the pipe due to friction will decrease by

Cold water flowing at $$0.1$$ $$kg/s$$ is heated from $${20^ \circ }C$$ to $${70^ \circ }C$$ in a counter-flow type heat exchanger by a hot water stream flowing at $$0.1$$ $$kg/s$$ and entering at $${90^ \circ }C$$. The specific heat of water is $$4200$$ $$J$$($$kg$$ $$K$$) and density is $$1000$$ $$kg/{m^3}.$$ If the overall heat transfer coefficient $$U$$ for the heat exchanger is $$2000$$ $$W/\,\,\left( {{m^2}\,\,K} \right),$$ the required heat exchange area (in $${{m^2}}$$) is