Question

Find an equation of the plane. The plane through the points (0, 9, 9), (9, 0, 9), and (9, 9, 0) Incorrect: Your answer is incorrect.

Answer 1

Answer:

The equation of the plane is represented by $\frac{1}{18}\cdot x + \frac{1}{18}\cdot y + \frac{1}{18}\cdot z = 1$.

Step-by-step explanation:

Algebraically speaking, a plane can be represented by following vectorial product:

$(a,b, c)\,\bullet\,(x,y,z) = 1$ (1)

Where:

$a$, $b$, $c$ - Plane coeffcients.

$x$, $y$, $z$ - Coordinates.

We need three distinct points to determine all coefficients. If we know that $(x_{1},y_{1},z_{1}) = (0,9,9)$, $(x_{2},y_{2}, z_{2}) = (9,0,9)$ and $(x_{3},y_{3},z_{3}) = (9,9,0)$, the system of equations to be solved is:

$9\cdot b + 9\cdot c = 1$ (1)

$9\cdot a + 9\cdot c = 1$ (2)

$9\cdot a + 9\cdot b = 1$ (3)

The solution of this system is $a = \frac{1}{18}$, $b = \frac{1}{18}$, $c = \frac{1}{18}$.

Hence, the equation of the plane is represented by $\frac{1}{18}\cdot x + \frac{1}{18}\cdot y + \frac{1}{18}\cdot z = 1$.