# Thread: Intercept Proof Tangent plane

1. ## 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!

2. ## Re: Intercept Proof Tangent plane

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: $\displaystyle y_0z_0(x-x_0)+x_0z_0(y-y_0)+x_0y_0(z-z_0)=0$

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

From the given we know that $\displaystyle x_0y_0z_0=1$

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