Find the vector equation of the plane that passes through the point (1, 0, 0) and contains the line r ^{ → } = โi ฬ j ฬ
Last updated at Oct. 27, 2020 by Teachoo
Transcript
Equation of plane passing through point A whose position vector is ๐ โ & perpendicular to ๐ โ is (๐ โ โ ๐ โ) . ๐ โ = 0 Given Plane passes through (1, 0, 0) So ๐ โ = 1๐ ฬ + 0๐ ฬ โ 0๐ ฬ ๐ โ = ๐ ฬ Thus, equation of plane is (๐ โ โ ๐ โ) . ๐ โ = 0 (๐ โ โ ๐ ฬ) . ๐ โ = 0 Now, The plane contains the line ๐ โ= ๐๐ ฬ So, Line is perpendicular to normal of plane ๐ ฬ . ๐ โ = 0 And, Lines point (0, 0, 0) lies on plane as well Putting ๐ โ = 0 โ in equation of plane (0 โ โ ๐ ฬ) . ๐ โ = 0 โ ๐ ฬ . ๐ โ = 0 ๐ ฬ . ๐ โ = 0 Since ๐ โ perpendicular to both ๐ ฬ and ๐ ฬ Thus, ๐ โ = ๐ ฬ So, our equation of plane becomes (๐ โ โ ๐ ฬ) . ๐ โ = 0 (๐ โ โ ๐ ฬ) . ๐ ฬ = 0 ๐ โ . ๐ ฬ โ ๐ ฬ . ๐ ฬ = 0 ๐ โ . ๐ ฬ = 0
CBSE Class 12 Sample Paper for 2021 Boards
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CBSE Class 12 Sample Paper for 2021 Boards
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