Elementary Geometry for College Students (6th Edition)

(a) $(x,y,z) = (7, 1, 1)$ (b) $(x,y,z) = (-14,16, -2)$
(a) We can use the line of intersection to find the value of $n$: $(x,y,z) = (0,6,0) + n(7,-5,1)$ Since $x = 7$, the $x$ coordinate in the line of intersection must be $7$: $0+n(7) = 7$ $n = 1$ We can use the line of intersection to find the point in both planes: $(x,y,z) = (0,6,0) + n(7,-5,1)$ $(x,y,z) = (0,6,0) + (1)(7,-5,1)$ $(x,y,z) = (0+7,6+(-5),0+1)$ $(x,y,z) = (7, 1, 1)$ (b) We can use the line of intersection to find the value of $n$: $(x,y,z) = (0,6,0) + n(7,-5,1)$ Since $y = 16$, the $y$ coordinate in the line of intersection must be $16$: $6+n(-5) = 16$ $n = -2$ We can use the line of intersection to find the point in both planes: $(x,y,z) = (0,6,0) + n(7,-5,1)$ $(x,y,z) = (0,6,0) + (-2)(7,-5,1)$ $(x,y,z) = (0-14,6+10,0-2)$ $(x,y,z) = (-14,16, -2)$