Vectors \[\vec{a} \text{ and } \vec{b}\] \[\left| \vec{a} \right| = \sqrt{3}, \left| \vec{b} \right| = \frac{2}{3}\text{ and } \left( \vec{a} \times \vec{b} \right)\] is a unit vector. Write the angle between \[\vec{a} \text{ and } \vec{b}\] .

\[\text{ Given } : \vec{a} \times \vec{b} \text{ is a unit vector } .\]\[ \Rightarrow \left| \vec{a} \times \vec{b} \right| = 1 . . . (1)\]\[\text{ Let} \theta \text{ be the angle between } \vec{a} \text{ and } \vec{b} . \]\[\text{ We know } \]\[\left| \vec{a} \times \vec{b} \right| = \left| \vec{a} \right| \left| \vec{b} \right| \sin \theta\]\[\text{ From (1), we get} \]\[1 = \left( \sqrt{3} \right) \left( \frac{2}{3} \right) \sin \theta \]\[ \Rightarrow \sin \theta = \frac{\sqrt{3}}{2}\]\[ \Rightarrow \theta = \frac{\pi}{3}\]

Vectors → a and → b | → a | = √ 3 , ∣ ∣ → b ∣ ∣ = 2 3 and ( → a × → b ) is a unit vector. Write the angle between → a and → b . - Mathematics

प्रश्न

Vectors $\vec{a} and \vec{b}$ $| \vec{a} | = \sqrt{3}, | \vec{b} | = \frac{2}{3} and (\vec{a} \times \vec{b})$ is a unit vector. Write the angle between $\vec{a} and \vec{b}$ .

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उत्तर

$Given : \vec{a} \times \vec{b} is a unit vector .$
$\Rightarrow | \vec{a} \times \vec{b} | = 1 . . . (1)$
$Let θ be the angle between \vec{a} and \vec{b} .$
$We know$
$| \vec{a} \times \vec{b} | = | \vec{a} | | \vec{b} | \sin θ$
$From (1), we get$
$1 = (\sqrt{3}) (\frac{2}{3}) \sin θ$
$\Rightarrow \sin θ = \frac{\sqrt{3}}{2}$
$\Rightarrow θ = \frac{π}{3}$

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

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Q 25 Q 24 Q 26

पाठ 25: Vector or Cross Product - very short answers [पृष्ठ ३४]

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आरडी शर्मा Mathematics [English] Class 12

पाठ 25 Vector or Cross Product
very short answers | Q 25 | पृष्ठ ३४

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Vectors → a and → b | → a | = √ 3 , ∣ ∣ → b ∣ ∣ = 2 3 and ( → a × → b ) is a unit vector. Write the angle between → a and → b . - Mathematics

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