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Question
Find the distance of the point whose position vector is `(2hat"i" + hat"j" - hat"k")` from the plane `vec"r" * (hat"i" - 2hat"j" + 4hat"k")` = 9
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Solution
Here `vec"a" = 2hat"i" + hat"j" - hat"k"`
`vec"n" = hat"i" - 2hat"j" + 4hat"k"`
And d = 9
So, the required distance is `(|(2hat"i" + hat"j" - hat"k") * (hat"i" - 2hat"j" + 4hat"k") - 9|)/sqrt(1 + 4 + 6)`
= `(|2 - 2 - 4 - 9|)/sqrt(21)`
= `13/sqrt(21)`.
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