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field h(x,y) = x^2 y

calculate gradient for this field and draw it for point (1,3):

calculate this point: nabla h = (2xy, x^2) = (2*1*3, 1) = (6, 1)

But how do I draw this into the field of x^2y? I know I have to draw a vector. Would this vector go from the middle towards (6, 1)?

Then: Imagine you walk in this field in the point (1,3) and you want to walk downhill at an angle of 45 degrees. Calculate the unit vector (is that the correct term?) that shows which direction to walk.

I know how to calculate the unit vector, but how do I put the 45 degrees into this?

Thanks a lot,

Hexa

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# Homework Help: Gradients and unit vectors

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