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Vector or Cross Product — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsVector or Cross Product3 Marks
Question
If $\big|\vec{\text{a}}\times\vec{\text{b}}\big|^2+\big|\vec{\text{a}}.\vec{\text{b}}\big|^2=400$ and $|\vec{\text{a}}|=5,$ then write the value of $\big|\vec{\text{b}}\big|.$
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Answer

$\big|\vec{\text{a}}\times\vec{\text{b}}\big|^2+\big|\vec{\text{a}}.\vec{\text{b}}\big|^2=400$ $\Rightarrow\Big\{|\vec{\text{a}}|\big|\vec{\text{b}}\big|\sin\theta\Big\}^2+\Big\{|\vec{\text{a}}|\big|\vec{\text{b}}\big|\cos\theta\Big\}^2=400$ $\Rightarrow|\vec{\text{a}}|^2\big|\vec{\text{b}}\big|^2\sin^2\theta+|\vec{\text{a}}|^2\big|\vec{\text{b}}\big|^2\cos^2\theta=400$ $\Rightarrow|\vec{\text{a}}|^2\big|\vec{\text{b}}\big|^2=400$ $\Rightarrow25\times\big|\vec{\text{b}}\big|^2=400$ $\Rightarrow\big|\vec{\text{b}}\big|^2=16$$\Rightarrow\big|\vec{\text{b}}\big|^2=4$

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