Answer
$x=-1-10t,y=1-16t,z=2-12t$
Work Step by Step
Our aim is to determine the tangent plane equation.
The general form is: $(x_2-x_1)f_x(x_1,y_1,z_1)+(y_2-y_1)f_y(x_1,y_1,z_1)+(z_2-z_1)f_x(x_1,y_1,z_1)=0$ ...(1)
From the given data, we have $f(x,y,z)=(-1,1,2)$
Equation (1), can be written as:
$\nabla P \times \nabla Q=\lt -2,2,-1 \gt \times \lt -8,2,4 \gt=\lt 10, 16, 12 \gt$
After simplifications, we get
$\dfrac{(x+1)}{5}=\dfrac{(y-1}{8}=\dfrac{(z-2)}{6}$
Therefore, the desired parametric line of equations are $x=-1-10t,y=1-16t,z=2-12t$
