# Intercept Proof Tangent plane

• Apr 29th 2013, 03:25 PM
topsaa
Intercept Proof Tangent plane
I've finished this problem and I got the tangent plane equation to be

Fx Fy Fz
Tangent plane(at Xo,Yo,Zo) = yo*zo(x-xo) + xo*zo(y-yo) + xo*yo(z-zo)

Not sure what the problem is asking in terms of the intercept, is it because if you multiply in Fx, Fy, Fz you get xo*yo*zo which would be the intercept?

Thanks!
• Apr 29th 2013, 04:37 PM
Plato
Re: Intercept Proof Tangent plane
Quote:

Originally Posted by topsaa
I've finished this problem and I got the tangent plane equation to be

Fx Fy Fz
Tangent plane(at Xo,Yo,Zo) = yo*zo(x-xo) + xo*zo(y-yo) + xo*yo(z-zo)

Not sure what the problem is asking in terms of the intercept, is it because if you multiply in Fx, Fy, Fz you get xo*yo*zo which would be the intercept?

Your plane should be written as: $y_0z_0(x-x_0)+x_0z_0(y-y_0)+x_0y_0(z-z_0)=0$

Now the $x\text{-intercept}$ of that plane is $(x_1,0,0)$ or
$y_0z_0(x_1-x_0)-x_0z_0y_0-x_0y_0z_0=0$

From the given we know that $x_0y_0z_0=1$

I admit I don't know exactly how to read the question beyond this point.