1. The problem statement, all variables and given/known data A plane has the equation aX + bY + cZ + d = 0. A line L goes from (0,0,0) and crosses the plane at some point. L and plane are orthogonal. express the coordinates of the crossing point P by: a, b, c and d. 2. Relevant equations |d|/sqrt(a^2 + b^2 + c^2) is the distance between point P and origo. [a,b,c] is the directional vector for the line and a normal vector on the plane. 3. The attempt at a solution So, if I divide [a,b,c] by the length of the directional vector, sqrt(a^2 + b^2 + c^2) and then multiply it by the length of the OP vector, |d|/sqrt(a^2 + b^2 + c^2), I get: a|d|/(a^2 + b^2 + c^2), b|d|/(a^2 + b^2 + c^2), c|d|/(a^2 + b^2 + c^2)=P. This is the crossing point of the line and the plane (or a point completely opposite to the plane). The answer is supposed to be (-ad/(a2 + b2 + c^2),-bd/(a2 + b2 + c2),-cd/(a2 + b2 + c2))=P I know that my answer is completely wrong, because |d| will remain always positive, while [a,b,c] could be negative or positive, with no consequence to |d|. Can somebody tell me how I can get to the correct answer?