Answer
a). The vector with largest magnitude can be created when they are in the same line, same direction and the angle between them is zero.
The magnitude is $=15+20=35cms$
b). The vector with minimum magnitude can be created when these 2 vectors are in same line, but opposite direction, the angle between them being $180^{\circ}$.
The magnitude will be =$20-15=5cms$
c). For any 2 vectors A and B,
$R^{2}=A^{2}+B^{2}+2ABcos\theta$
Where R is the magnitude of the resultant vector.
So, R can be maximum, when $cos\theta=+1$, so that $R=A+B$
And R can be minimum, when $cos\theta=-1$, so that $R=A-B$
Work Step by Step
The two displacements are having magnitudes 15 cm and 20 cm.
a). The vector with largest magnitude can be created when they are in the same line, same direction and the angle between them is zero.
The magnitude is $=15+20=35cms$
b). The vector with minimum magnitude can be created when these 2 vectors are in same line, but opposite direction, the angle between them being $180^{\circ}$.
The magnitude will be =$20-15=5cms$
c). For any 2 vectors A and B,
$R^{2}=A^{2}+B^{2}+2ABcos\theta$
Where R is the magnitude of the resultant vector.
So, R can be maximum, when $cos\theta=+1$, so that $R=A+B$
And R can be minimum, when $cos\theta=-1$, so that $R=A-B$
