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Answer:
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
Step-by-step 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
