If [bar{a} bar{b} bar{c}] = 4,then the volume | vedclass

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(D) The volume of a parallelepiped with coterminal edges $\vec{u}, \vec{v}, \vec{w}$ is given by the scalar triple product $[\vec{u} \vec{v} \vec{w}]

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(D) The volume of a parallelepiped with coterminal edges $\vec{u}, \vec{v}, \vec{w}$ is given by the scalar triple product $[\vec{u} \vec{v} \vec{w}] = \vec{u} \cdot (\vec{v} 	imes \vec{w})$.Given $[\bar{a} \bar{b} \bar{c}] = \bar{a} \cdot (\bar{b} 	imes \bar{c}) = 4$.We need to find the volume of the parallelepiped with edges $\vec{u} = \bar{a} + 2 \bar{b}$,$\vec{v} = \bar{b} + 2 \bar{c}$,and $\vec{w} = \bar{c} + 2 \bar{a}$.Volume $= [(\bar{a} + 2 \bar{b}) (\bar{b} + 2 \bar{c}) (\bar{c} + 2 \bar{a})]$.Using the property of scalar triple products,$[\bar{a} + 2 \bar{b}, \bar{b} + 2 \bar{c}, \bar{c} + 2 \bar{a}] = [\bar{a} \bar{b} \bar{c}] + 8 [\bar{b} \bar{c} \bar{a}] = [\bar{a} \bar{b} \bar{c}] + 8 [\bar{a} \bar{b} \bar{c}] = 9 [\bar{a} \bar{b} \bar{c}]$.Substituting the given value: $9 	imes 4 = 36$ cubic units.

If $[\bar{a} \bar{b} \bar{c}] = 4$,then the volume (in cubic units) of the parallelepiped with $\bar{a} + 2 \bar{b}, \bar{b} + 2 \bar{c}$ and $\bar{c} + 2 \bar{a}$ as coterminal edges,is

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