Question

The equation of the plane through the points (0,1,8),(1,1,11) and (1,6,0) is:

z= Blank 1. Calculate the answer by read surrounding text.

+ Blank 2. Calculate the answer by read surrounding text.

x+ Blank 3. Calculate the answer by read surrounding text.

y.

Answer 1

$A(0,1,8), B(1,1,11), C(1,6,0)\\ \begin{vmatrix} x-0 & y-1&z-8 \\ 1-0 & 1-1&11-8\\ 1-0&6-1&0-8 \end{vmatrix}=0\\ \begin{vmatrix} x & y-1&z-8 \\ 1 & 0&3\\ 1&5&-8 \end{vmatrix}=0\\ x\cdot \begin{vmatrix} 0 & 3 \\ 5 & -8 \end{vmatrix}-(y-1)\cdot \begin{vmatrix} 1 & 3 \\ 1 & -8 \end{vmatrix}+\\+(z-8)\cdot \begin{vmatrix} 1 & 0 \\ 1 & 5 \end{vmatrix}=0\\ (0-15)x-(y-1)(-8-3)+\\+(z-8)(5-0)=0\\ -15x+11(y-1)+5(z-8)=0\\ -15x+11y+5z-51=0$