In ΔABC
(A) $\vec{AB}+\vec{BC}+\vec{CA}=\vec{O}$
(B) $\vec{AB}+\vec{BC}-\vec{AC}=\vec{O}$
(C) $\vec{AB}+\vec{BC}-\vec{CA}=\vec{O}$
(D) $\vec{AB}-\vec{CB}+\vec{CA}=\vec{O}$
(E) $\vec{AB}-\vec{CB}-\vec{CA}=\vec{O}$
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 1
in given triangle $\vec{A B}+\vec{B C}=\vec{A C}$ by triangular of vector addition.
so $\vec{A B}+\vec{B C}-\vec{A C}=\vec{0}$
⇒ $\vec{A B}+\vec{B C}+\vec{C A}=\vec{0}$ as $\vec{A C}= -\vec{C A}$
⇒ $\vec{A B}-\vec{C B}+\vec{C A}=\vec{0}$ as $\vec{B C}= -\vec{C B}$