Finding a unit vector that gives the maximum directional derivative of a vector field

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This is a question that I don't really know if I did it right.

A vector field is given, and a point. Its gradient is $9i+12j+3k$. It will be biggest at when there is no angle, so $\cos(0)$.

Is the formula $$\left(\frac{\vec v}{|v|}\right)=\left(\frac{\|gradf|}{gradf}\right)$$ correct? And if so, I get a scalar devided by a vector, I'm not sure how to proceed

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The gradient of a scalar function is a vector that shows the direction of the maximum of increase. So the vector that shows the direction of the maximum directional derivative is the gradient itself. The unit vector in the direction of the gradient will be $$\frac{\vec{v}}{\vert \vec{v}\vert}=\frac{\mathrm{grad}\,f}{\vert\mathrm{grad}\,f\vert}$$ I hope this helps.