The perpendicular distance between the line `vecr = 2hati-2hatj+3hatk+lambda(hati-hatj+4hatk)` and the plane `vecr.(hati + 5hatj + hatk) = 5` is :

Options

A. `10/3`
B. `3/10`
C. `10/(3sqrt(3))`
D. `10/9`

Answer

C

Explanation

Clearly, given line passes through the point `(2hati-2hatj-3hatk)` and is parallel to the given plane.
`:.` Distance between the line and the plane
`=` Length of perpendicular from `2hati-2hatj+3hatk` to the given plane.
`=(|(2hati-2hatj+3hatk).(hati+5hatj+hatk)-5|)/(|hati+5hatj+hatk|)=10/(3sqrt(3))`