Give a condition that the three vectors $straight a with rightwards arrow on top comma space straight b with rightwards arrow on top space and space straight c with rightwards arrow on top$ form the three sides of a triangle. What are the other possibilities?

Let $OA with rightwards arrow on top space equals space straight a with rightwards arrow on top comma space space AB with rightwards arrow on top space equals space straight b with rightwards arrow on top comma space space space BO with rightwards arrow on top space equals space straight c with rightwards arrow on top$
Now, $OA with rightwards arrow on top space plus space AB with rightwards arrow on top space equals space OB with rightwards arrow on top$
$therefore space space space space space space space straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top space equals space minus straight c with rightwards arrow on top therefore space space space space space straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top space plus space straight c with rightwards arrow on top space equals space 0 with rightwards arrow on top$
Other possibilities are
$straight a with rightwards arrow on top space equals space straight b with rightwards arrow on top plus straight c with rightwards arrow on top comma space$
$straight b with rightwards arrow on top space equals space straight c with rightwards arrow on top space plus space straight a with rightwards arrow on top comma space space space straight c with rightwards arrow on top space equals space straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top$

Other possibilities are
$straight a with rightwards arrow on top space equals space straight b with rightwards arrow on top space plus space straight c with rightwards arrow on top comma straight b with rightwards arrow on top space equals space straight c with rightwards arrow on top space plus space straight a with rightwards arrow on top comma space space straight c with rightwards arrow on top space equals space straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top$

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Give a condition that the three vectors form the three sides of a triangle. What are the other possibilities?

Vector Algebra

Mathematics Part II

Give a condition that the three vectors $straight a with rightwards arrow on top comma space straight b with rightwards arrow on top space and space straight c with rightwards arrow on top$ form the three sides of a triangle. What are the other possibilities?