Question

If three conterminous edges of a parallelopiped are represented by $\mathbf{a} - \mathbf{b},\mathbf{b} - \mathbf{c}$ and $\mathbf{c} - \mathbf{a}$, then its volume is

• A. [a b c]
• B. 2 [a b c]
• C. $\lbrack\mathbf{abc}\rbrack^{2}$
• D. 0

Answer 1

Answer: (D)

0

Answer 2

$(\mathbf{a} - \mathbf{b}).(\mathbf{b} - \mathbf{c}) \times (\mathbf{c} - \mathbf{a}) = (\mathbf{a} - \mathbf{b}).(\mathbf{b} \times \mathbf{c} - \mathbf{b} \times \mathbf{a} + \mathbf{c} \times \mathbf{a})$

$= \mathbf{a}.(\mathbf{b} \times \mathbf{c}) - \mathbf{a}.(\mathbf{b} \times \mathbf{a}) + \mathbf{a}.(\mathbf{c} \times \mathbf{a}) - \mathbf{b}.(\mathbf{b} \times \mathbf{c}) + \mathbf{b}.(\mathbf{b} \times \mathbf{a}) - \mathbf{b}.(\mathbf{c} \times \mathbf{a})$ =0.