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I have a homework question asking to find the equation for a line that passes through the point A(-1,0,2) and that is parallel to the planes 2x-y+z=5 and x+2y-z-4=0 does anybody know how to figure this out?

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HINT

Notice that the normal vectors are given by $\textbf{n}_{1} = (2,-1,1)$ and $\textbf{n}_{2} = (1,2,-1)$. Therefore the line's direction is given by the cross product $\textbf{n}_{1}\times\textbf{n}_{2}$.

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  • $\begingroup$ Once you have a location and a direction you have a line. $\endgroup$ – ja72 Jul 18 '17 at 21:41
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The Direction Ratios of the line is equal to cross product of the normals of both planes Hence you will get the Direction ratios and then write it in the equation of line as you are already given the points it passes through.

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