Question

There are two force vectors, one of $5N$ and other of $12N$. At what angle the two vectors be added to get resultant vector of $17N$, $7N$ and $13N$ respectively

• A. $0^{\circ },{180}^{\circ }$and ${90}^{\circ }$
• B. $0^{\circ },{90}^{\circ }$ and ${180}^{\circ }$
• C. $0^{\circ },{90}^{\circ }$ and ${90}^{\circ }$
• D. ${180}^{\circ },0^{\circ }$ and ${90}^{\circ }$

Answer 1

The correct option is A $0^{\circ },{180}^{\circ }$and ${90}^{\circ }$

${\overrightarrow{F}}_1=5N$ and ${\overrightarrow{F}}_2=12N$
Since, ${\overrightarrow{F}}_1+{\overrightarrow{F}}_2=17$
Therefore, for resultant to be $17N$ both the vector should be parallel i.e. angle between them should be $0^{\circ }$
Since, ${\overrightarrow{F}}_1+(-{\overrightarrow{F}}_2)=7$
Therefore, for resultant to be $7N$ in terms of magnitude both the vectors should be antiparallel i.e. angle between them should be ${180}^{\circ }$
Since, $\sqrt{F_1^2+F_2^2}=\sqrt{5^2+{12}^2}=13$
Therefore, for resultant to be $13N$ both the vectors should be perpendicular to each other i.e. angle between them should be ${90}^{\circ }$