A vector ` vec n` of magnitude 8 units is inclined to x-axis at `45^0` , y-axis at `60^0` and an acute angle with z-axis. If a plane passes through a point `(sqrt(2),-1,1)` and is normal to ` vec n` , find its equation in vector form.

Explanation

Given,

`l=cos(45)^0=1/(sqrt2) ,m-=cos(60)^0=1/2,n=cosalpha`

We know that,

`=l^2+m^2+n^2=1`

`=(cos(45)^0)^2+(cos(60)^0)^2+n^2=1`

`=1/2+1/4+n^2=1`

`=n=1/2`

So,

...