If $\vec{a}+\vec{b}=\vec{c}$ and $a+b=c$, then the angle included between $\vec{a}$ and $\vec{b}$ is

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Professor PC Thomas Classes · Answer

(d): Here, $\vec{a}+\vec{b}=\vec{c}$ and $c=a+b$ Let $	heta$ be angle between $\vec{a}$ and $\vec{b}$. $ \ 	herefore \quad c=\sqrt{a^2+b^2+2 a b \cos 	heta} ; a+b=\sqrt{a^2+b^2+2 a b \cos 	heta} \ $ Squaring both sides, we get \ $(a+b)^2=a^2+b^2+2 a b \cos 	heta$\ $a^2+b^2+2 a b=a^2+b^2+2 a b \cos 	heta$\ $2 a b-2 a b \cos 	heta=0$ or $1-\cos 	heta=0$\ $\cos 	heta=1$ or $	heta=\cos ^{-1}(1)=0^{\circ}$