Find direction numbers for the line of intersection of the p

Find direction numbers for the line of intersection of the planes

x + y + z = 6 and x + z = 0.

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Solution

Find direction numbers for the line of intersection of the planes

x + y + z = 6 and x + z = 0.

Plug in x + z with 0 :

y + 0 = 6

y = 6

From x + z = 0, we have z = -x

So, the parametric equations of the line are :

x = t , y = 6 , z = -t

So, the vector equations are :

<x,y,z> = <0,6,0> + t<1,0,-1>

So, the direction numbers are : <1 , 0 , -1>

Answer ---> <1 , 0 , -1>