Question

Find the equation of the plane in the form z = c + mx + ny containing the line in the xy-plane where y = 8, and the line in the xz-plane where z = 3

Answer 1

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Answer 2

Given:

z = c + mx + ny

line in the xy-plane: y = 8

line in the xz-plane: z = 3

To Find:

The equation

Solution:

The plane containing the lines y=8 and z=3 in the xy-plane and the xz-plane, respectively, are both independent of x

Therefore, we can fix x=0

$\frac{z}{3} + \frac{y}{8} = 1$

$\frac{z}{3} = 1 - \frac{y}{8}$

$z = 3 - \frac{3y}{8}$

where c = 0, m = 0 and n = -3/8

the equation of the plane in the form z = c + mx + ny containing the line in the xy-plane where y = 8, and the line in the xz-plane where z = 3 is z = 3 - (3y/8).