1. ## Direction numbers question

Could someone please tell me how to find the "the set of direction numbers" [1,-1,1]? I get everything else in that question but I don't recall at all how to find these. (Question, solution and answer attached).

Any help would be greatly appreciated!

2. ## Re: Direction numbers question

The set of "direction numbers" is the direction vector of the equation of the normal line. When they took the gradient of the surface (The partial derivatives), they evaluated them at the point (1,2,1)

This gives

$\displaystyle \frac{\partial F}{\partial x}\bigg|_{(1,2,1)}= -2, \frac{\partial F}{\partial y}\bigg|_{(1,2,1)}= 2, \frac{\partial F}{\partial z}\bigg|_{(1,2,1)}= -2$

This gives the direction vector $\displaystyle -2\mathbf{i}+2\mathbf{j}-2\mathbf{k}$ Since they all have a commond factor of "2" the direction vector is the same as $\displaystyle -\mathbf{i}+\mathbf{j}-\mathbf{k}$ the coeffiecents give you the "direction numbers"

3. ## Re: Direction numbers question

Thanks!

Just to say though, ∂F/∂z = -2 != 2 but I got the point.

4. ## Re: Direction numbers question

Originally Posted by s3a
Thanks!

Just to say though, ∂F/∂z = -2 != 2 but I got the point.
Thanks I will fix the above. The funny thing is I typed the correct vector after! haha