Question

Let V be the volume of the parallelopiped formed by the vectors a = a1i + a2j + a3k, b = b1i + b2j + b3k and c = c1i + c2j + c3k. If ar, br, cr where r = 1, 2, 3, are non-negative real numbers and (ar + br + cr) for ∑∈ [r=1,3] = 3L, Show that V ≤ L3.

Answer 1

We have,

V = [a b c]

Thus,