Now on another question, that states four points in space have 4 position vectors a,b,c and d relative to O. The question tells you that the line O to the mid-point of AB, BC and CD is perpendicular to the lines AB, BC and CD respectively. The question is asking for me to prove that therefore a^2 = b^2 = c^2 = d^2. Now I have used that fact that the dot product of the perpendicular lines = 0 which ends up proving that the coefficients of the vectors a and b for example equal each other. But is this proof that the actual vectors equal each other? Is there a better way of doing it without using the dot product? Hope I have explained this well enough.Thanks.