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VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA1 Mark
Question
Find $|\overrightarrow{\text{x}}|,$ if for a unit vector $\overrightarrow{\text{a}},(\overrightarrow{\text{x}} - \overrightarrow{\text{a}}).(\overrightarrow{\text{x}} + \overrightarrow{\text{a}}) = 15.$
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Answer

Given $(\overrightarrow{\text{x}} - \overrightarrow{\text{a}}).(\overrightarrow{\text{x}} + \overrightarrow{\text{a}})= 15 $
$\Rightarrow(\overrightarrow{\text{x}})^{2} - (\overrightarrow{\text{a}})^{2} = 15 $
$\Rightarrow\overrightarrow{\text{x}}.\overrightarrow{\text{x}} - \overrightarrow{\text{a}}.\overrightarrow{\text{a}} = 15 \Rightarrow|\overrightarrow{\text{x}}|^{2} - |\overrightarrow{\text{a}}|^{2} = 15 $
$\Rightarrow|\overrightarrow{\text{x}}|^{2} - 1 = 15 \Rightarrow|\overrightarrow{\text{x}}|^{2} = 16$
$\Rightarrow|\overrightarrow{\text{x}}| = 4 [\because - \text{ ve value is not acceptable}].$

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