1. The problem statement, all variables and given/known data Find the vector equation of the line that passes through the point Q(2,0,-5) and is perpendicular to both the vectors m=(0,1,4) and n=(-2,-1,3). 2. Relevant equations vector equation of a line: (x, y, z)=(x0,y0,z0) + t(a,b,c) cartesian equation of a line: (x-x0)/a=(y-y0)/b=(z-z0)/c 3. The attempt at a solution (x0,y0,z0)=(2,0,5) To find (a,b,c)I know I can get two equations because the dot product of (a,b,c) with the two perpendicular lines equals zero: b+4c=0 -2a-b+3c=0 But two equations isn't enough to solve for three variables. Also, shouldn't the point (2,0,-5) also dot product with u or v to equal zero, since it's on the same line? Is it correct to assume that the points (0,1,4) and (-2,-1,3) are also points on the line? In which case I can easily find the direction of the line by subtracting one from the other.