Given vectors →a=12^i+√32^j, →b=√32^j+12^k and →c=^i+2^j+3^k. Then the volume of a parallelepiped with three coterminous edges as →u=(→a⋅→a)→a+(→a⋅→b)→b+(→a⋅→c)→c, →v=(→a⋅→b)→a+(→b⋅→b)→b+(→b⋅→c)→c and →w=(→a⋅→c)→a+(→b⋅→c)→b+(→c⋅→c)→c equals

Given vectors →a=12^i+√32^j, →b=√32^j+12^k and →c=^i+2^j+3^k

1.	Given vectors →a=12^i+√32^j, →b=√32^j+12^k and →c=^i+2^j+3^k. Then the volume of a parallelepiped with three coterminous edges as →u=(→a⋅→a)→a+(→a⋅→b)→b+(→a⋅→c)→c, →v=(→a⋅→b)→a+(→b⋅→b)→b+(→b⋅→c)→c and →w=(→a⋅→c)→a+(→b⋅→c)→b+(→c⋅→c)→c equals
Answer» Given vectors $\to a = \frac{1}{2}^i + \frac{\sqrt{3}}{2}^j,$ $\to b = \frac{\sqrt{3}}{2}^j + \frac{1}{2}^k$ and $\to c =^i + 2^j + 3^k .$ Then the volume of a parallelepiped with three coterminous edges as $\to u = (\to a \cdot \to a) \to a + (\to a \cdot \to b) \to b + (\to a \cdot \to c) \to c,$ $\to v = (\to a \cdot \to b) \to a + (\to b \cdot \to b) \to b + (\to b \cdot \to c) \to c$ and $\to w = (\to a \cdot \to c) \to a + (\to b \cdot \to c) \to b + (\to c \cdot \to c) \to c$ equals