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VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA1 Mark
Question
State True or False for the following:
The formula $(\vec{\text{a}}+\vec{\text{b}})=\vec{\text{a}}^2+\vec{\text{b}}^2+2\vec{\text{a}}\times\vec{\text{b}}$ is valid for non-zero vectors $\vec{\text{a}}$ and $\vec{\text{b}}.$
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Answer

False.Solution:
$(\vec{\text{a}}+\vec{\text{b}})=(\vec{\text{a}}+\vec{\text{b}})\cdot(\vec{\text{a}}+\vec{\text{b}})$
$(\vec{\text{a}}+\vec{\text{b}})=\vec{\text{a}}^2+\vec{\text{b}}^2+2\vec{\text{a}}\cdot\vec{\text{b}}$

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