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Vector or Cross Product — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSVector or Cross Product3 Marks
Question
If $|\vec{\text{a}}|=2,\big|\vec{\text{b}}\big|=5$ and $\big|\vec{\text{a}}\times\vec{\text{b}}\big|=8,$ find $\vec{\text{a}}.\vec{\text{b}}.$
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Answer

We know
$\big(\vec{\text{a}}.\vec{\text{b}}\big)^2+\big|\vec{\text{a}}\times\vec{\text{b}}\big|^2=|\vec{\text{a}}|^2\big|\vec{\text{b}}\big|^2$
$\Rightarrow\big(\vec{\text{a}}.\vec{\text{b}}\big)^2+8^2=2^2\times5^2$ $\big(\therefore\big|\vec{\text{a}}\times\vec{\text{b}}\big|=8,|\vec{\text{a}}|=2$and $\big|\vec{\text{b}}\big|=5\big)$
$\Rightarrow\big(\vec{\text{a}}.\vec{\text{b}}\big)^2+64=100$
$\Rightarrow\big(\vec{\text{a}}.\vec{\text{b}}\big)^2=36$
$\Rightarrow\big(\vec{\text{a}}.\vec{\text{b}}\big)=6$

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