Question

What is the unit vector that is normal to the plane containing 3i+7j-2k and 8i+2j+9k?

Answer 1

The unit vector normal to the plane is
`(1/94.01)(67hati-43hatj+50hatk)`.

Explanation:

Let us consider `vecA=3hati+7hatj-2hatk, vecB= 8hati+2hatj+9hatk`
The normal to the plane `vecA, vecB` is nothing but the vector perpendicular i.e., cross product of `vecA, vecB`.
#=>vecAxxvecB= hati(63+4)-hatj(27+16)+hatk(6-56) =67hati-43hatj+50hatk#.
The unit vector normal to the plane is
`+-[vecAxxvecB//(|vecAxxvecB|)]`
So`|vecAxxvecB|=sqrt[(67)^2+(-43)^2+(50)^2]=sqrt8838=94.01~~94`
Now substitute all in above equation, we get unit vector =`+-{[1/(sqrt8838)][67hati-43hatj+50hatk]}`.