Question

Find a normal vector and an equation for the tangent plane to the surface:

x³ - y² - z² - 2xyz + 6 =0

at the point P : (−2, 1, 3). Determine the equation of the line formed by the
intersection of this plane with the plane x = 0.

[10 marks]
(b) Find the directional derivative of the function F(x, y, z) = 2x /zy² , at  the

point P : (1, −1, −2) in the direction of the vector

~v =

2
1
−3
Give a

brief interpretation of what your result means.

Answer 1

Find a normal vector and an equation for the tangent plane to the surface x3-y2-z2-2xyz +6-0 at the point P: (2, 1,3) Determine the equation of the line formed by the intersection of this plane with the planex -0 ах (b) Find the directional derivative of the function F(x, y, z)-2x/zy2, at the point P: (1,-1,-2) in the direction of the vector v- (2 1-3) Give a brief interpretation of what your result means The directional derivative of f (z, y, z) in the direction of the unit vector u(a, b,c) is given by 2 4-1リ 14- 04 ナ 5