If → a , → B , → C Are Three Non-coplanar Mutually Perpendicular Unit Vectors, Then [ → a → B → C ] , is - Mathematics

प्रश्न

If $\vec{a,} \vec{b,} \vec{c}$ are three non-coplanar mutually perpendicular unit vectors, then $[\vec{a} \vec{b} \vec{c}],$ is

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उत्तर

$\pm 1$

We have

$[\vec{a} \vec{b} \vec{c}]$

$= (\vec{a} \times \vec{b}) . \vec{c}$

$= | \vec{a} \times \vec{b} | | \vec{c} | \cos 0^{\circ} or | \vec{a} \times \vec{b} | | \vec{c} | c o s 180^{\circ} (∵ \vec{a}, \vec{b,} \vec{c} are perpendicular to each other)$

$= | \vec{a} \times \vec{b} | o r - | \vec{a} \times \vec{b} | (∵ | \vec{c} | = 1, c o s 0^{\circ} = 1 and \cos 180^{\circ} = - 1)$

$= | \vec{a} | | \vec{b} | \sin 90^{\circ} or - | \vec{a} | | \vec{b} | \sin 90^{\circ} (∵ {\vec{a}}^{} is perpendicular to \vec{b})$

$= 1 or - 1 (∵ | \vec{a} | = 1 and | \vec{b} | = 1)$

$= \pm 1$

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Scalar Triple Product of Vectors

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अध्याय 26: Scalar Triple Product - MCQ [पृष्ठ १८]

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अध्याय 26 Scalar Triple Product
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Scalar Triple Product of Vectors

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If → a , → B , → C Are Three Non-coplanar Mutually Perpendicular Unit Vectors, Then [ → a → B → C ] , is - Mathematics

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If → a , → B , → C Are Three Non-coplanar Mutually Perpendicular Unit Vectors, Then [ → a → B → C ] , is - Mathematics

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