In [itex]ℝ^{3}[/itex], how would I go about proving that two planes are parallel, given their equations? I know what the "word" parallel means, in the sense that two planes are always equidistant from one another, so that they must either never intersect, or that they must intersect at every point on their graphs.(adsbygoogle = window.adsbygoogle || []).push({});

But how does this translate to an algebraic, or vector definition of parallel planes, given the equations for both planes?

Say the equation for plane 1 is [itex] a_{1}x + b_{1}y + c_{1}z = d_{1} [/itex] and the equation for plane 2 is [itex] a_{2}x + b_{2}y + c_{2}z = d_{2} [/itex].

Under what conditions would they be paralle, given the geometric definitions of parallel I have just given?

Or are my definitions just incorrect?

BiP

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# Proving that planes are parallel

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