Question

Two vectors have magnitudes 3 unit and 4 unit respectively. What should be the angle between them if the magnitude of the resultant is 5 unit

• A. ${30}^{\circ }$
• B. $0^{\circ }$
• C. ${180}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is D

${90}^{\circ }$

$|\overrightarrow{R}|=5$

$|\overrightarrow{R}{|}^2$ = 25 = $|\overrightarrow{A}{|}^2$ + $|\overrightarrow{B}{|}^2$ + 2 $|\overrightarrow{A}|$$|\overrightarrow{B}|$ cos $\theta$

= $3^2+4^2+2\left(3\right)\left(4\right)cos\theta$

= $9+16+24cos\theta$

= 25 + 24 cos $\theta$

$\Rightarrow 24cos\theta =0$

$\Rightarrow cos\theta =0$

$\Rightarrow \theta ={90}^{\circ }$

$\therefore$ The angle between them is ${90}^{\circ }$

We can clearly see that as 3,4 and 5 is a Pythagorean triplet , they will always from a right angled triangle.