( 717, #39 ) Find direction numbers for the line of intersection of the planes
x + y + z = 1 and x + z = 0.

Solution: Since the line lies in both planes, we have y = 1 for:

From the equation x + z = 0 we have z = -x. Thus the parametric equations of the line are:

x = t, y = 1, z = -t

The vector equations are:

< x, y, z > = < 0, 1, 0 > + t < 1, 0, -1 >

The direction numbers of this line are 1, 0 and -1.

By: nl