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

Answer 1

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)`.