Equation of the normal plane to a curve

[e^x]

My teacher told me my answers to 1 and 2 are correct. For 1 I got (1.875, 0, ln0.5). For 2 I got x = 1 - 3t, y = 1 + 2t, and z = t. However, I don't know how to use this information to solve for 3

 

[blamocur]

It might help to remember that "normal to C" means normal to the C's tangent.

 

[e^x]

It might help to remember that "normal to C" means normal to the C's tangent.

Hmmm... so are the coefficients of the ts in the parametric equations of the tangent lines the coefficients of the plane?

 

[blamocur]

Hmmm... so are the coefficients of the ts in the parametric equations of the tangent lines the coefficients of the plane?

I would think so. I don't know whether your teacher expects normalized vectors in the equation. And, of course, you have to make that the plane contains the (1,1,0) point.

 

[blamocur]

I would think so. I don't know whether your teacher expects normalized vectors in the equation. And, of course, you have to make that the plane contains the (1,1,0) point.

...you have to make sure that the plane contains the (1,1,0)...