Statement $I:$ If three forces $\vec{F}_{1}, \vec{F}_{2}$ and $\vec{F}_{3}$ are represented by three sides of a triangle and $\overrightarrow{{F}}_{1}+\overrightarrow{{F}}_{2}=-\overrightarrow{{F}}_{3}$, then these three forces are concurrent forces and satisfy the condition for equilibrium.
Statement $II:$ A triangle made up of three forces $\overrightarrow{{F}}_{1}, \overrightarrow{{F}}_{2}$ and $\overrightarrow{{F}}_{3}$ as its sides taken in the same order, satisfy the condition for translatory equilibrium.
In the light of the above statements, choose the most appropriate answer from the options given below:
Statement$-I$ is false but Statement$-II$ is true
Statement$-I$ is true but Statement$-II$ is false
Both Statement$-I$ and Statement$-II$ are false
Both Statement$-I$ and Statement$-II$ are true.
The vectors $\overrightarrow A $ and $\overrightarrow B$ lie in a plane. Another vector $\overrightarrow C $ lies outside this plane. The resultant $\overrightarrow A + \overrightarrow B + \overrightarrow C$ of these three vectors
Prove the associative law of vector addition.
Let $\overrightarrow C = \overrightarrow A + \overrightarrow B$
$(A)$ It is possible to have $| \overrightarrow C | < | \overrightarrow A |$ and $ | \overrightarrow C | < | \overrightarrow B|$
$(B)$ $|\overrightarrow C |$ is always greater than $|\overrightarrow A |$
$(C)$ $|\overrightarrow C |$ may be equal to $|\overrightarrow A | + |\overrightarrow B|$
$(D)$ $|\overrightarrow C |$ is never equal to $|\overrightarrow A | + |\overrightarrow B|$
Which of the above is correct
Two forces of magnitude $P$ & $Q$ acting at a point have resultant $R$. The resolved part of $R$ in the direction of $P$ is of magnitude $Q$. Angle between the forces is :