QJEEM22Mafcc8: JEE Main 2022 Physics - Class 11 JEEM22Mafcc8 Solution: Let a → and b → be two vectors such that

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QJEEM22Mafcc8: JEE Main 2022 Physics - Class 11 JEEM22Mafcc8 Solution: Let a → and b → be two vectors such that

Let $\vec{a}$ and $\vec{b}$ be two vectors such that $| \vec{a} + \vec{b} |^{2} = | \vec{a} |^{2} + 2 | \vec{b} |^{2}, \vec{a} \cdot \vec{b} = 3$ and $| \vec{a} \times \vec{b} |^{2} = 75$ . Then $| \vec{a} |^{2}$ is equal to __________.

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\because|\vec{a}+\dot{b}|^{2}=|\vec{a}|^{2}+2|b|^{2}

or

|\vec{a}|^{2}+|\vec{b}|^{2}+2 \vec{a} \cdot \vec{b}=|\vec{a}|^{2}+2|\vec{b}|^{2}

\therefore|\vec{b}|^{2}=6

Now

|\vec{a} \times \vec{b}|^{2}=|\vec{a}|^{2}|\vec{b}|^{2}-(\vec{a} \cdot \vec{b})^{2}

75 = | \vec{a} |^{2} \cdot 6 - 9

\therefore|\vec{a}|^{2}=14

QJEEM22Mafcc8: JEE Main 2022 Physics - Class 11 JEEM22Mafcc8 Solution: Let a → and b → be two vectors such that

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