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Numerade Educator

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Problem 49 Easy Difficulty

Find direction numbers for the line of intersection of the planes $ x + y + z = 1 $ and $ x + z = 0 $.

Answer

$<1,0,-1>$

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Video Transcript

no. Well we have a question and then we need to find direction numbers of the lineup in protection of the plains. So planes are being given the exploits of why I said equal to one and second is explains that equal to zero. So direction number or direction issue of this is like I let's say place K As coefficient of X is one one and one. And direction the issue of this is one. Place uh coefficient of X is one. So simply I less there is no J because term of Y is not here to simply okay required number of line of intersections of plans Will be equal to cross product of these two. I place mhm Place care that is a gap. Mhm into I bless K. We'll just find out cross products. This is I the K coefficient at 111 101. Okay so this is I. and one into 1 is 1 0 and 20 minus J. Because we'll go like plus minus plus minority and one and 2 one is 1 -1 into one is 1 plus cake up zero into 10 -1. So this is I kept brand zero minus taken. I kept mindscape cups for direction numbers will be one 00:00 -1 because the school building has one into a Plus zero in 2 K Plus -1 into K. Camp Sure one is here zero is here and -1 is here. This will be the required direction number. Thank you