Find the distance of the point `P(3,8,2)` from the line `1/2(x-1)=1/4(y-3)=1/3(z-2)` measured parallel to the plane `3x+2y-2z+15=0.`

Explanation

Let the general point of the line be `A(2lamda+1, 4lamda+3, 3lamda+2)`.
Let this point lie on the line such that AP is parallel to the plane. Then
`" "vec(AP)bot(3hati+2hatj-2hatk)`
or `" "3*(2lamda-2)+2(4lamda-5)-2(3lamda)=0`
or `" "lamda=2`
Therefore, `A` is (5, 11, 8).
`" "PA=sqrt((5-3)^(2)+(11-8)^(2) +(8-2)^(2))`
`" "=sqrt(4+9+36)=7`