just help me to check homework on vector calculus :)

denian

Find the equation of the normal vector, tangent plane, and the normal line to
the graph of the equation at point P.

here's the equation and my solution:




please help me verify if my answer is correct. tqvm!

HallsofIvy

Do you understand that most people are not going to download a file from someone they don't know?

denian

sorry. changed it to jpeg. :)

HallsofIvy

Yes, very nicely done!

Those of us who dislike fractions (third grade trauma!) might prefer

2x- y+ 2z= 0 for the tangent plane (multiply your equation by -2) and
[2t, 2- 2t, 1+ 2t] for the normal line (replace your t by -2t) but your equations are completely correct.

denian

HoI, thank you very much!