Question

Magnitudes of four pairs of displacement vectors are given. Which pair of displacement vectors, under vector addition, fails to give a resultant vector of magnitude $3\,cm$ ?

• A. $2\,cm,7\,cm$
• B. $1\,cm,4\,cm$
• C. $2\,cm,3\,cm$
• D. $2\,cm,4\,cm$

Answer 1

Answer: (A)

$2\,cm,7\,cm$

Answer 2

If two vectors $A$ and $B$ are given the range of their resultant can be written as
$(A-B)\le (A+B)$
ie, $R_{\max }=A+B$ and $R_{\min }=A-B$
If $B=7$ and $A=2,$
then their resultant will be in between $5$ and $9$. So,
$3\,cm$ cannot be the resultant of the pair.