# Thread: slope of line at interesection of 2 planes

1. ## slope of line at interesection of 2 planes

Consider the line where the planes z=1+2x+3y and y=2x intersect. It can be given by the parametric equation x=t, y=2t and z=1+2t+3(2t). Find the slope of this line in the direction of increasing t.

I haven't learned vectors.

I took the derivatives
x'=1
y'=2
z'=8

2. Originally Posted by superdude
Consider the line where the planes z=1+2x+3y and y=2x intersect. It can be given by the parametric equation x=t, y=2t and z=1+2t+3(2t). Find the slope of this line in the direction of increasing t.

I haven't learned vectors.

I took the derivatives
x'=1
y'=2
z'=8

Now you have to evaluate the directional deriviative, but it is worthless since you haven't studied vectors which, by the way, ashtonishes me since then you shouldn't be given this kind of questions.

Tonio

3. $\displaystyle \frac{\Delta z}{distance}=\frac{17-1}{\sqrt{1^2+2^2}}=\frac{16}{sqrt{5}}$

can anyone verrifiy this for me?