Question

A scalar function $\varphi$ is defined by $\varphi =y^2-x^2$ then the magnitude of the gradient at point (2,3).

• A. 7.21
• B. 5.21
• C. 9.21
• D. 6.21

Answer 1

The correct option is A 7.21

grad$\varphi =▽\varphi =-2x\hat{i}+2y\hat{j}$

$(▽\varphi {)}_{(2,3)}=-4\hat{i}+6\hat{j}$

$|▽\varphi |=\sqrt{16+36}=\sqrt{52}=2\sqrt{13}=7.21$