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Question Number 130780 by LYKA last updated on 28/Jan/21

Commented by kaivan.ahmadi last updated on 29/Jan/21

$$\overrightarrow{b}=(2,-1,1)\Rightarrow \mid \overrightarrow{b}\mid =\sqrt{6}\Rightarrow \overrightarrow{u}=\frac{\overrightarrow{b}}{\mid \overrightarrow{b}\mid }=(\frac{2}{\sqrt{6}},\frac{-1}{\sqrt{6}},\frac{1}{\sqrt{6}})$$$$▽f=(3x^2-3yz,3y^2-3xz,3z^2-3xy)$$$$▽f{\mid }_{(-1,0,1)}=(3,3,3)$$$$D_{\overrightarrow{u}}f(x,y,z)=\overrightarrow{u}.▽f\left(b\right)=\sqrt{6}-\frac{\sqrt{6}}{2}+\frac{\sqrt{6}}{2}=\sqrt{6}$$

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