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Find direction numbers for the line of intersection of the planes x + y + z = 7 and x + z = 0. (enter your answers as a comma-separated list.)

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sqdancefan

The line of intersection has a direction vector that is the cross product of the normal vectors of the given planes.

... [1, 1, 1] × [1, 0, 1] = [1, 0, -1] . . . . . . using a suitable calculator


The direction numbers of the line of intersection are (1, 0, -1).

yoodyannapolis

We have given equation of planes as

Plane 1: [tex]x+y+z=7[/tex]

Plane 2: [tex]x+z=0[/tex]

That is

[tex]m=[/tex][tex]< 1, 1, 1 >[/tex]

[tex]n=<1,0,1>[/tex]

Line direction numbers is

[tex]m[/tex] × [tex]n[/tex] =[tex]< 1, 1, 1 >[/tex] ×[tex]< 1, 0, 1 >[/tex]

= [tex]< 1, 0, 1 >[/tex]

Therefore direction numbers for the line of intersection of the planes [tex]x + y + z = 7[/tex] and[tex]x + z = 0[/tex] is[tex]<1,0,1>[/tex].

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