is the surface of the box enclosed by the planes where are positive numbers.
D) 12
E) 12

Question

is the surface of the box enclosed by the planes  where  are positive numbers.
D) 12 
E) 12

Quizplus · Accepted Answer

Each plane has an equation of the form Ax + By + Cz + D = 0, where A, B, and C are the coefficients of x, y, and z, and D is a constant. Since we know the planes have positive coefficients, we can write each plane as z = (-A/B)x + (-C/B). Therefore, we want to find the intersection of the three planes, which is the point where all three equations are equal. Solving each pair of equations gives us the following system:

(-A/B)x + (-C/B) = (-D/E)y + (-F/E)
(-A/B)x + (-C/B) = (-G/H)z + (-J/H)
(-D/E)y + (-F/E) = (-G/H)z + (-J/H)

Solving this system yields x = EJ/(BFH), y = DH/(BEF), and z = EF/(BDH). Plugging in the given values of A, B, C, D, E, F, G, H, and J and simplifying gives us the answer choice C.

Is the Surface of the Box Enclosed by the Planes