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If \vec{a}+\vec{b}=\vec{c}\And a+b=c then the angle included between \vec{a}\And \vec{b}

Option: 1

{{90}^{\circ }}


Option: 2

{{180}^{\circ }}


Option: 3

{{120}^{\circ }}


Option: 4

Zero


Answers (1)

best_answer

Here, \vec{a}+\vec{b}=\vec{c}\And a+b=c

Let \theta be the angle between \vec{A}\And \vec{B}

c=\sqrt{{{a}^{2}}+{{b}^{2}}+2ab\cos \theta } \\ a+b=\sqrt{{{a}^{2}}+{{b}^{2}}+2ab\cos \theta } \\

Squaring both sides we get,
{{(a+b)}^{2}}={{a}^{2}}+{{b}^{2}}+2ab\cos \theta \\ {{a}^{2}}+{{b}^{2}}+2ab={{a}^{2}}+{{b}^{2}}+2ab\cos \theta \\ 2ab-2ab\cos \theta =0 \\ 2ab(1-\cos \theta )=0 \\ (1-\cos \theta )=0 \\ \cos \theta =1 \\ \theta ={{\cos }^{-1}}(1) \\ \theta =0 \\

Posted by

Devendra Khairwa

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