Question

Find the vector equation of a plane at a distance 6 units from the origin and to which vector `2hat"i" - hat"j" + 2hat"k"` is normal

Answer 1

Let `bar"n" = 2hat"i" - hat"j" + 2hat"k"`

∴ `hat"n"` is the unit vector along normal

∴ `hat"n" = (bar"n")/|bar"n"|`

= `(2hat"i" - hat"j" + 2hat"k")/sqrt(2^2 + (-1)^2 2 ^2)`

= `(2hat"i" - hat"j" + 2hat"k")/sqrt(4 + 1 + 4)`

= `(2hat"i" - hat"j" + 2hat"k")/3`

and p = 6

 Vector equation of plane is `bar"r"*hat"n"` = p

∴ `bar"r"*((2hat"i" - hat"j" + 2hat"k"))/3` = 6

∴ `bar"r"*(2hat"i" - hat"j" + 2hat"k")` = 18