Question

The magnitudes of four pairs of displacement vectors are given. Which pair of displacement vectors cannot be added to give a resultant vector of magnitude 4 cm?

• A. 1 cm, 1 cm
• B. 1 cm, 3 cm
• C. 1 cm, 5 cm
• D. 1 cm, 7 cm

Answer 1

Answer: (A), (D)

1 cm, 7 cm

The magnitude R of the resultant of two vectors A and B depends upon the magnitudes of A and B and the angle $\theta$ between them and is given by
$R^2=A^2+B^2+2ABcos\theta$
When $\theta =0$, R is maximum given by
$R_{max}^2=A^2+B^2+2AB$
or, $R_{max}=A+B$
When $\theta ={180}^0$, R is minimum given by
$R_{max}^2=A^2+B^2-2AB$
or, $R_{min}=A-B$
Thus, the magnitude of resultant will lie between A – B and A + B.
Hence the correct choices are (a) and (d).