Write a unit vector perpendicular to \[\hat{ i } + \hat{ j } \text{ and } \hat{ j } + \hat{ k } .\]

\[\text{ Let } \vec{a} = \hat{ i } + \hat{ j } + 0 \hat{ k } ; \vec{b} = 0 \hat{ i } + \hat{ j } + \hat{ k } \]\[ \vec{a} \times \vec{b} = \begin{vmatrix}\hat{ i } & \hat{ j } & \hat{ k } \\ 1 & 1 & 0 \\ 0 & 1 & 1\end{vmatrix}\]\[ = \hat{ i } - \hat{ j } + \hat{ k } \]\[ \Rightarrow \left| \vec{a} \times \vec{b} \right| = \sqrt{1 + 1 + 1}\]\[ = \sqrt{3}\]\[\text{ Unit vector perpendicular to } \vec{a} \text{ and } \vec{b} \text{ is } ,\frac{\vec{a} \times \vec{b}}{\left| \vec{a} \times \vec{b} \right|} = \frac{1}{\sqrt{3}}\left( \hat{ i } - \hat{ j } + \hat{ k } \right)\]

Write a Unit Vector Perpendicular to ^ I + ^ J and ^ J + ^ K . - Mathematics

प्रश्न

Write a unit vector perpendicular to $\hat{i} + \hat{j} and \hat{j} + \hat{k} .$

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उत्तर

$Let \vec{a} = \hat{i} + \hat{j} + 0 \hat{k}; \vec{b} = 0 \hat{i} + \hat{j} + \hat{k}$
$\vec{a} \times \vec{b} = | \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & 1 & 0 \\ 0 & 1 & 1 \end{matrix} |$
$= \hat{i} - \hat{j} + \hat{k}$
$\Rightarrow | \vec{a} \times \vec{b} | = \sqrt{1 + 1 + 1}$
$= \sqrt{3}$
$Unit vector perpendicular to \vec{a} and \vec{b} is, \frac{\vec{a} \times \vec{b}}{| \vec{a} \times \vec{b} |} = \frac{1}{\sqrt{3}} (\hat{i} - \hat{j} + \hat{k})$

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Product of Two Vectors - Vector (Or Cross) Product of Two Vectors

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पाठ 25: Vector or Cross Product - very short answers [पृष्ठ ३३]

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पाठ 25 Vector or Cross Product
very short answers | Q 16 | पृष्ठ ३३

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Write a Unit Vector Perpendicular to ^ I + ^ J and ^ J + ^ K . - Mathematics

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Write a Unit Vector Perpendicular to ^ I + ^ J and ^ J + ^ K . - Mathematics

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