Find the volume of parallelopiped whose edges are OA -3-1-4- OB -1-2-3- OC -2-1-5

O⃗A⃗=(3,1,4) O⃗B⃗=(1,2,3) O⃗C⃗=(2,1,5) Volume =[O⃗A⃗ O⃗B⃗ O⃗C⃗]=3 amp;1 amp;4 1 amp;2 amp;3 2 amp;1 amp;5=10 ...

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Applications of Dot Product

Find the volu...

Question

Find the volume of parallelopiped whose edges are $- - \to O A = (3, 1, 4), - - \to O B = (1, 2, 3), - - \to O C = (2, 1, 5)$

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- - \to O A = 2^i - 3^j + 0^k,

- - \to O B =^i +^j -^k

- - \to O C = 3^i - 3^k

O A = 2 i - 3 j,

O B = i + j - k, O C = 3 i - k

O A = a, O B = b, O C = c

\to a = 2^i - 3^j - 4^k, \to b =^i + 2^j -^k,

\to c = 3^i +^j + 2^k

¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c

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