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Calculus/vector calculus

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Expert: - 4/27/2008


Question
Consider the surface z = f(x,y).  Confirm that
m = (-fx,-fy,1)  is normal to the surface and that
u = (1,0,fx)     v = (0,1,fy),  
are both orthogonal to m, without being parallel to each other.  Hence deduce that
r = r0 + su +tv
are parametric equations of the tangent plane at r0.

Answer
Two vectors are said to be perpendicular if the dot product is zero.

Two points are parallel if u = cv where u, v are vectors and c is a constant.

The equation for point on the plane containing u and v is then the equation given by r = r0 + st + tv where r0 is the point on the plane where the curve touches the plane.

Thanks for the question and I hope this helps.  Thanks for the score.

Calculus

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Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

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