I have that P is the tangent plane to the surface xyz=a[tex]^{3}[/tex] at the point (r,s,t). I need to show that the volume of the tetrahedron, T, formed by the coordinate planes and the tangent plane to P is indepedent of the point (r,s,t).(adsbygoogle = window.adsbygoogle || []).push({});

I have found that P is;

[tex]\frac{x}{r}[/tex] + [tex]\frac{y}{s}[/tex] + [tex]\frac{z}{t}[/tex] = 3

A know that the volume of a tetrahedron is giving by 1/3(area of base [tex]\times[/tex] height)

But I just can't picture what this looks like, as far as I can see the volume of T has to be dependent of the point (r,s,t).

Any help anyone could give would be great! Thanks.

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# Volume of tetrahedra formed from coordinate and tangent planes

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