I am new to vector calculus.
I watched few you tube videos and came to the conclusion that directional derivative is something like slope with direction and its value is scalar while gradient of a scalar is the vector which has magnitude and direction as that of directional derivative.Is my understanding correct.Please correct me if i am wrong.It would be great if you can point me some wonderful simple resource (any text book or video resource ) on which i can better understand the concept
Now i stumbled upon this exercise in one of my college text books
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I hardly understand this question what does $||\nabla f(x,y,z) || $ mean ..how come k becomes $\frac{5}{3}$ ..Which formula of is used here.Any help and suggestion will be highly appreciated .Thanks and regards in advance.
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