Parallel, perpendicular, and angle between planes (KristaKingMath)

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Learn how to determine whether two planes are parallel or perpendicular, and if the planes are neither parallel nor perpendicular, then to find the angle between the planes. If the planes are parallel, then their normal vectors are parallel. If the planes are perpendicular, then their normal vectors are perpendicular. Therefore, take the coefficients on the x, y and z terms and these are the components of the normal vectors. Set the ratio of the component values equal to each other and if the equation is true, then the normal vectors are parallel and therefore the planes are parallel. Find the dot product of the normal vectors and if the dot product is zero, then the normal vectors are perpendicular so the planes are perpendicular. If the planes are neither parallel nor perpendicular, then use the corollary formula to find the angle between the planes.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com

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