Question

Example Find the equation of the tangent plane and the normal line at the point (1,1,1) to the surface 2x2 + 2y2 + 3z2 = 6. Example Find the equation of the tangent plane and the normal line at the point (1, 2, 3) to the surface 2x2 + y2 – z2 = -3.

Partial derivatives

Answer 1

... 24 ²4 24 ² 4 3 2 ² 0 = 6 (1,1,1) f(x4, 2) = 94² 4 2 4 ² 4 372 : 6 = 0 of foulazy?+372–6] - Fre 476 Fotot0 = 426 Fulllil) & 4 Fy = 2 ( 24 24 24² + 37² -6.] Fy = 4y f2 = 2 ( 22 ²4 24² 43 7²6]. F = 62 Eliela 6 : F(1, 1, 1) = 212 + 3-6 = 1 la of tangent plane Fe (1), )) (u-ro) + Fy (),1,1) 19-9.) + F2 [1,11) (2-20) = 0 4 (-1) + 414-1) + 6(2-1)=0

Franco Page: Normal line is ģit) = {1,1,1 > t t < 4,4,6> (1) 211461044; 1+6+ > 1 Ex- 2 .-? - 3 012,3) F. (19, 2) = 2u ?y? z 23=0 Fre (x, y, z) = g ure - Fel 1,2,3) = 4 fych.4, 2) - 2 y y (1,2,3) = 4 Ez (m14, 2) = -2 z F2 L 1,2,3) = -6 eqh of tangent plane is 1462-1) 4 (7-2) -6 (7-3) = 0 Normal line is ñ (t) = 21,2,3> t t < 4,4-67 (t) = L eut, 2+4 t 3-6t>