Question

Hello guys , please answer this question and explain the answer.

Answer 1

we know, resultant of two vectors $\vec{A}$ and $\vec{B}$ is given by,
$R=\sqrt{A^2+B^2+2ABcos\theta}$
where $\theta$ is the angle between vectors A and B.

we also know, maximum value of $cos\theta$ = 1
then, maximum value of R = |A + B|
and Minimum value of $cos\theta$ = -1
so, minimum value of R = |A - B|

e.g., |A - B| ≤ R ≤ |A + B| , use this concept here .

we have given resultant , R = 15N
so, |A - B| ≤ 15 ≤ | A + B|

check options , you get only option (a) is satisfied because |A - B| = |20 - 20| = 0.
|A + B| = | 20 + 20| = 40.
here, 0 ≤ 15 ≤ 40

hence answer is option (a)