Give a condition that three vectors ` vec a , vec b` and ` vec c` from the three sides of a triangle. What are the other possibilities?

Explanation

Let A B C be a triangle such that `vec{B C}=vec{d} vec{A B}=vec{c} `and `vec{C A}=vec{b}`.
Then, quad `bar{d}+vec{b}+vec{c}=vec{B C}+vec{C A}+vec{A B} vec{a}+vec{b}+vec{c}=vec{B A}+vec{A B}`

`[: vec{B C}+vec{C A}=vec{B A}]`

`Rightarrow vec{a}+vec{b}+vec{c}=vec{B B}`

[Using triangle law]

`Rightarrow vec{a}+vec{b}+vec{c} rightarrow=vec{0}`

[ By definition of null vector]

Other possibilities are

(i) `vec{c}+vec{d}=vec{b}`

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