(a) Show that two vectors are orthogonal if the magnitude of their sum is equal to the magnitude of their difference. (b) The usual Cartesian coordinate system is said to be right-handed as the choice of coordinate axes corresponds the productˆx׈y=ˆz, which follow from the right-hand rule. Ina diagram, for instance, once the placement of two axes are chosen, the third is determined by the right-hand rule (it is not an arbitrary choice). If instead a left-handed coordinate system is desired, by what constant can the unit vectors be multiplied to yield, for instance,ˆx′׈y′=−ˆz′(where these primed unit vectors correspond to the left-handed coordinate system)? Use this product to derive the constant and corroborate your results by computingˆy′׈z′andˆz′׈x′.