Question

A scalar of temperature T is given by, T= x2 + y2 +z2 . Calculate the gradient (∇T) of the scalar function at (1, 1, 2).

Answer 1

$\nabla\ T=\frac{\partial T}{\partial x}\overrightarrow{i}+\frac{\partial T}{\partial y}\overrightarrow{j}+\frac{\partial T}{\partial z}\overrightarrow{k}=$

$=2x\overrightarrow{i}+2y\overrightarrow{j}+2z\overrightarrow{k}=2\cdot1\cdot \overrightarrow{i}+2\cdot1\cdot \overrightarrow{j}+2\cdot2\cdot \overrightarrow{k}=$

$=2\cdot \overrightarrow{i}+2\cdot \overrightarrow{j}+4\cdot \overrightarrow{k}$ . Answer