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Scalar Or Dot Product — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsScalar Or Dot Product2 Marks
Question
If two vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ are such that $|\vec{\text{a}}|=2,\big|\vec{\text{b}}\big|=1$ and $\vec{\text{a}}.\vec{\text{b}}=1,$ then find the value of $\big(3\vec{\text{a}}-5\vec{\text{b}}\big).\big(2\vec{\text{a}}+7\vec{\text{b}}\big).$
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Answer

$\big(3\vec{\text{a}}-5\vec{\text{b}}\big).\big(2\vec{\text{a}}+7\vec{\text{b}}\big)$
$=3\vec{\text{a}}.2\vec{\text{a}}+3\vec{\text{a}}.7\vec{\text{b}}-5\vec{\text{b}}.2\vec{\text{a}}-5\vec{\text{b}}.7\vec{\text{b}}$
$=6\vec{\text{a}}.\vec{\text{a}}+21\vec{\text{a}}.\vec{\text{b}}-10\vec{\text{a}}.\vec{\text{b}}-35\vec{\text{b}}.\vec{\text{b}}$
$=6|\vec{\text{a}}|^2+11\vec{\text{a}}.\vec{\text{b}}-35\big|\vec{\text{b}}\big|^2$
$=6\times2^2+11\times1-35\times1^2$
$=35-35$
$=0$

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