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Vector Addition

Find the volu...

Question

Find the volume of the parallelepiped whose coterminous edges are represented by vectors $\to a =^i +^j +^k; \to b = 2^i + 4^j -^k$ and $\to c =^i +^j + 3^k$

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Solution

The correct option is A $4$
The volume of the parallelepiped

$= ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 2 & 4 & - 1 1 & 1 & 3 \end{matrix} ∣ ∣ ∣ ∣$

$= 1 (12 + 1) - 1 (6 + 1) + 1 (2 - 4)$

$= 13 - 7 - 2 = 13 - 9 = 4$ cubic units.

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\to a, \to b, \to c

\to a, & \to b

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| (\to a \times \to b) \times (\to c \times \to d) |

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\to a + \to b + \to c = 4^i - 4^j

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

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\sqrt{78}

\to a, \to b, \to c

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

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