Find equations of the tangent plane and normal line to the surface at the point (-8, 0, 0).
Tangent Plane: (make the coefficient of z equal to 1).
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Normal line: ____,____
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Thanks!
Take $\displaystyle F(x,y,z) = xe^y \cos z - z$
the tangent plane is given by: $\displaystyle F_x(-8, 0, 0)(x + 8) + F_y(-8, 0, 0)(y - 0) + F_z(-8, 0, 0)(z - 0) = 0$
the normal line is given by: $\displaystyle \left< -8,0,0 \right> + t \left< \text{normal vector to the above plane} \right>$