First, you should be able to see that the line (x- 10)/4= y/3= z/2, which is the same as the line given by parametric equations, x= 10+ 4t, y= 3t, z=2t, has direction vector <4, 3, 2>. Further, any line through (0, 0, 0) to (a, b, c) can be written as x= as, y= bs, z= cs and has direction vector <a, b, c>. If the two lines are perpendicular, then their dot product, <4, 3, 2>.<a, b, c>= 4a+ 3b+ 2c= 0. Since the two lines intersect, we can take (a, b, c) to be a line on the given line and so must satisfy the equation: (a- 10)/4= b/3= c/2. That gives two equations for a, b, and c. Since we only want the equation of the line, and not a specific point, it is sufficient to solve for either of two unknows in terms of the other one, then choose a convenient value for it.