Let $P(a,b,c)$ be a point and let a line pass through $(x_1,y_1,z_1)$ with direction ratios $(d,m,n)$. If $\vec{AP}=(a-x_1,\; b-y_1,\; c-z_1)$ where $A=(x_1,y_1,z_1)$, then the perpendicular distance from $P$ to the line is

Let $\vec v=(a-x_1, b-y_1, c-z_1)$ and direction vector of the line be $\vec u=(d,m,n)$. The squared distance from the point to the line equals the squared length of $\vec v$ minus the squared length of the projection of $\vec v$ on $\vec u$. Therefore, $$ \text{distance}=\sqrt{|\vec v|^2-\frac{(\vec v\cdot \vec u)^2}{|\vec u|^2}} $$ which gives option C. Option A is the magnitude of the scalar projection, not the perpendicular distance; option B is just the distance from the given point on the line; option D has the wrong dimension.