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Vector Algebra — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSVector Algebra1 Mark
Question
Fill in the blanks.
If $|\vec{\text{a}}\times\vec{\text{b}}|^2+|\vec{\text{a}}\cdot\vec{\text{b}}|^2=144$ and $|\vec{\text{a}}|=4,$ then $|\vec{\text{b}}|^2$ is equal to ________.
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Answer

If $|\vec{\text{a}}\times\vec{\text{b}}|^2+|\vec{\text{a}}\cdot\vec{\text{b}}|^2=144$ and $|\vec{\text{a}}|=4,$ then $|\vec{\text{b}}|^2$ is equal to 3.Solution:
$|\vec{\text{a}}\times\vec{\text{b}}|^2+|\vec{\text{a}}\cdot\vec{\text{b}}|^2=144$ $|\vec{\text{a}}|^2|\vec{\text{b}}|^2\sin^2\theta+|\vec{\text{a}}|^2|\vec{\text{b}}|^2\cos^2\theta=144$ $\Rightarrow|\vec{\text{a}}|^2|\vec{\text{b}}|^2=144$ $\Rightarrow|\vec{\text{a}}|^2|\vec{\text{b}}|^2=12$ $\Rightarrow4|\vec{\text{b}}|^2=12$ $\Rightarrow|\vec{\text{b}}|^2=3$

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