In a triangle ABC (shown in the figure below) | vedclass

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(A) Based on the triangle law of vector addition,for a triangle $ABC$ with the given directions:$(i)$ By the triangle law,$\vec{AB} + \vec{BC} = \vec{

Vedclass · Accepted Answer

$(i)$ True,(ii) True,(iii) True,(iv) False

Vedclass · Answer

(A) Based on the triangle law of vector addition,for a triangle $ABC$ with the given directions:$(i)$ By the triangle law,$\vec{AB} + \vec{BC} = \vec{AC}$.Rearranging gives $\vec{AB} + \vec{BC} - \vec{AC} = \vec{0}$.Since $\vec{AC} = -\vec{CA}$,we have $\vec{AB} + \vec{BC} + \vec{CA} = \vec{0}$. Thus,$(i)$ is True.(ii) From the triangle law,$\vec{AB} + \vec{BC} = \vec{AC}$,which implies $\vec{AB} + \vec{BC} - \vec{AC} = \vec{0}$. Thus,(ii) is True.(iii) We have $\vec{AB} + \vec{BC} = \vec{AC}$. Also,$\vec{CB} = -\vec{BC}$,so $\vec{BC} = -\vec{CB}$.Substituting this into the first equation: $\vec{AB} - \vec{CB} = \vec{AC}$.Rearranging gives $\vec{AB} - \vec{CB} - \vec{AC} = 0$,or $\vec{AB} - \vec{CB} + \vec{CA} = 0$. Thus,(iii) is True.(iv) From $(i)$,$\vec{AB} + \vec{BC} = -\vec{CA} = \vec{AC}$.Then $\vec{AB} + \vec{BC} - \vec{CA} = \vec{AC} - \vec{CA} = \vec{AC} + \vec{AC} = 2\vec{AC} 
eq \vec{0}$. Thus,(iv) is False.Therefore,the correct sequence is $(i)$ True,(ii) True,(iii) True,(iv) False.

In a $\triangle ABC$ (shown in the figure below),state whether the following are true or false:
$(i)$ $\vec{AB} + \vec{BC} + \vec{CA} = \vec{0}$
(ii) $\vec{AB} + \vec{BC} - \vec{AC} = \vec{0}$
(iii) $\vec{AB} - \vec{CB} + \vec{CA} = \vec{0}$
(iv) $\vec{AB} + \vec{BC} - \vec{CA} = \vec{0}$

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In a $\triangle ABC$ (shown in the figure below),state whether the following are true or false:$(i)$ $\vec{AB} + \vec{BC} + \vec{CA} = \vec{0}$(ii) $\vec{AB} + \vec{BC} - \vec{AC} = \vec{0}$(iii) $\vec{AB} - \vec{CB} + \vec{CA} = \vec{0}$(iv) $\vec{AB} + \vec{BC} - \vec{CA} = \vec{0}$