Question

what will be it condition?
If IA+ B|^2=A² +B² ​

Answer 1

Required Answer

we know,

$\sf |A+B | = {\sqrt{A {}^{2} + {B}^{2} + 2 AB \cos \theta } }$

Solution :

$\sf \:\:\:\:\:\:\:\:\:\:\:| A+ B|^2=A² +B²$

$\sf \implies \bigg({\sqrt{A {}^{2} + {B}^{2} + 2 AB \cos \theta } } \bigg) ^{2} = { A}^{2} + {B}^{2}$

$\sf \implies {{ \cancel{A {}^{2}} + \cancel{ {B}^{2} }+ 2 AB \cos \theta } } ^{} = \cancel{ { A}^{2}} + \cancel{{B}^{2} }$

$\sf \implies \cos \theta = 0$

$\: \: \: \therefore \: \: \: \underline{ \boxed{ \mathfrak{ \theta = (n\pi + \frac{\pi}{2} )}}} \: \: \bf n \in\N$

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