Question

If$\vec{a}=\vec{b}+\vec{c}$, then is it true that |$\vec{a}$|=|$\vec{b}$|+|$\vec{c}$| ? justify your answer.

Answer 1

In $△ABC$,let $\overrightarrow{CB}=\vec{a},\overrightarrow{CA}=\vec{b},$and $\overrightarrow{AB}=\vec{c}$(as shown in the following figure).

Now,by the triangle law of vector addition,we have $\vec{a}=\vec{b}+\vec{c}$.
It is clearly known that |$\vec{a}$|,|$\vec{b}$|,and |$\vec{c}$|represent the sides of $△ABC.$
Also,it is known that the sum of the lengths of any two sides of a triangle is greater than the third side.
∴|$\vec{a}$|<|$\vec{b}$|+|$\vec{c}$|
|Hence,it is not true that |$\vec{a}$|=|$\vec{b}$|+|$\vec{c}$|.