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If I have a surface x^{2}+3y^{2}+2z^{2}=9, how am I suppose to find all the unit magnitude vectors that are tangential to the surface at point (-1,0,9)?

So far, I am able to find the normal vector 2xi+6yj+4zkand the equation of the plane at (-1,0,9) will therefore be 2x+6y+4z=6. However, then I am stuck and I do not know how can I find the unit magnitude vectors that are tangential to the surface.

Can someone please help me?

Thanks in advance.

Casey.

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# Tangential vector of a surface

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