Question

3 vectors $\overline{a},\overline{b},\overline{c}$ can always form the sides of a triangle if $\overline{a}+\overline{b}+\overline{c}=0$

• A. True
• B. False

Answer 1

The correct option is B

False

The given condition is valid only when the 3 vectors or are not collinear. For instance consider the situation in which $\overline{a}=\hat{i}+\hat{j}+\hat{k},b=2\hat{i}+2\hat{j}+2\hat{k},c=-(3\hat{i}+3\hat{j}+3\hat{k})$. In this case we can still have $\overline{a}+\overline{b}+\overline{c}=0$ but they lie along the vector $\hat{i}+\hat{j}+\hat{k}$.

But in case when no 2 of the given vectors are parallel and the given condition is valid then we can say they do form sides of a triangle. Therefore the given statement is not always true.