Question

yz = 7ln(x + z), (0, 0, 1) (a) the tangent plane Correct: Your answer is correct. (b) parametric equations of the normal line to the given surface at the specified point. (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.)

Answer 1

The equation of tangent plane is 7x - y + 7z - 7 = 0

Parametric equation of normal line

x = 7 t , y=-t , z=1+7 t

Explanation:

Equation of tangent

fₓ (x₀ , y₀ , z₀) (x-x₀) + fy (x₀ , y₀ , z₀) (y-y₀) +fz(x₀ , y₀ , z₀)(z-z₀)=0 (1)

From taking derivation we get

fₓ (x₀ , y₀ , z₀) = 7

fy (x₀ , y₀ , z₀)= -1

fz(x₀ , y₀ , z₀) = 7

putting these value in equation 1

(7) (x-0) + (-1)(y-0) + 7(z-1)=0

7x - y + 7z - 7 = 0

The equation of tangent plane is 7x - y + 7z - 7 = 0

b) Parametric equation

x=x +f ₓ (P)t , y = y₀ +f y (P) t , z=z₀ +f z (P) t

x=0 +7 t , y =0+(-1) t , z=1+7 t

x=7 t ,y=-t , z= 1+7 t

Parametric equation of normal line

x = 7 t , y=-t , z=1+7 t