Answer:
The standard equation is 8x+3y+4z= -24.
Step-by-step explanation:
Given : The general equation of a plane is Ax + By + Cz = D, where A, B, C, and D are real numbers and A is non negative.
We have to find the equation of the plane containing the points (3, 0, 0), (0, 8, 0), and (0, 0, 6).
If given coordinates of three points \(A(x_1, y_1, z_1), B(x_2, y_2, z_2),C(x_3, y_3, z_3)\) lying on a plane are defined then the plane equation can be found using the formula,
\(\left[\begin{array}{ccc}x - x_1&y-y_1&z-z_1\\x_2 - x_1&y_2-y_1&z_2-z_1\\x_3 - x_1&y_3-y_1&z_3-z_1\end{array}\right]=0\)
For the given coordinates, A(3, 0, 0), B(0, 8, 0), and C(0, 0, 6)
Substitute, we have,
\(\begin{pmatrix}x-3&y-0&z-0\\ \:0-3&8-0&0-0\\ \:0-3&0-0&6-0\end{pmatrix}=0\)
Solving further, we get,
\(\begin{pmatrix}x-3&y&z\\ \:-3&8&0\\ \:-3&0&6\end{pmatrix}=0\)
Evaluate along row !, we get,
\((x-3)(8\cdot6-0) -y((-3)\cdot6-0)+z(0-8\cdot (-3))\)
We get,
\(48(x-3)+18y+24z=0\)
Simplify , we get,
\(8x+3y+4z -24 = 0\)
Thus, the standard equation is 8x+3y+4z= -24
