Question

What are the $3$conditions for formation of triangle by $3$vectors?

Answer 1

Define conditions for formation of a triangle.

The conditions for formation of a triangle by $3$vectors is as follows:

1. All three vectors should have different directions. From the figure, we can clearly see that if $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ will have same direction we can't construct a triangle from parallel vectors, they should have different directions.
2. The sum of the magnitude of two of the vectors must be greater than the magnitude of the third one. i.e.$\left|\overrightarrow{c}\right|<\left|\overrightarrow{a}\right|+\left|\overrightarrow{b}\right|$.
3. The magnitude of the sum of two vectors is equal to the magnitude of the third. i.e. $\left|\overrightarrow{c}\right|=\left|\left(\overrightarrow{a}+\overrightarrow{b}\right)\right|$.