Question

There are two force vectors, one of $5N$ and other of $12N$. At what angle the two vectors be added to get a 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 $0^{\circ },{180}^{\circ }and{90}^{\circ }$

Here, $\overrightarrow{R}=\overrightarrow{A}+\overrightarrow{B}$

or $\overrightarrow{R}.\overrightarrow{R}=(\overrightarrow{A}+\overrightarrow{B}).(\overrightarrow{A}+\overrightarrow{B})$

or $R^2=A^2+B^2+2AB\cos \theta$ where $\theta$ be the angle between vectors A and B.

When $R=17N\Rightarrow {17}^2=5^2+{12}^2+2\left(5\right)\left(12\right)\cos \theta$ or $cos\theta =1=cos0$ or $\theta =0^o$

When $R=7N\Rightarrow 7^2=5^2+{12}^2+2\left(5\right)\left(12\right)\cos \theta$ or $cos\theta =-1=cos180$ or $\theta ={180}^o$

When $R=13N\Rightarrow {13}^2=5^2+{12}^2+2\left(5\right)\left(12\right)\cos \theta$ or $cos\theta =0=cos90$ or $\theta ={90}^o$