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  • Let  be the angle between the vectors <img alt="\vec{a} \text { and } \vec{b}" src="https://entranc

Let \theta be the angle between the vectors \vec{a} \text { and } \vec{b}, where |\overrightarrow{\mathrm{a}}|=4,|\overrightarrow{\mathrm{b}}|=3 \text { and } \theta \in\left(\frac{\pi}{4}, \frac{\pi}{3}\right) \text {. } Then |(\vec{a}-\vec{b}) \times(\vec{a}+\vec{b})|^{2}+4(\vec{a} \cdot \vec{b})^{2} \text { is equal to }___________.

Option: 1

576


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

|(\vec{a}-\vec{b}) \times(\vec{a}+\vec{b})|^{2}+4(\vec{a} \cdot \vec{b})^{2}
=|-\vec{b} \times \vec{b}-\vec{b} \times \vec{a}+\vec{a} \times \vec{b}+\vec{a} \times \vec{a}|^{2}+4(\vec{a} \cdot \vec{b})^{2}
=4\left[|\vec{a} \times \vec{b}|^{2}+(\vec{a}. \vec{b})^{2}\right] =4|\vec{a}|^{2}|\vec{b}|^{2}
                                                  =4 \times 9 \times 16
                                                   =576

Posted by

vishal kumar

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