Question

For three vectors $p,q$ and $r$, if $r=3p+4q$ and $2r=p-3q$, then

• A. $|r|<2|q|$ and $r,q$ have the same direction
• B. $|r|>2|q|$ and $r,q$ have opposite directions
• C. $|r|<2|q|$ and $r,q$ have opposite directions
• D. $|r|>2|q|$ and $r,q$ have the same direction

Answer 1

Answer: (B)

We have, $r=3p+4q...(i)$
and $2r=p-3q...(ii)$
On eliminating $p$, from Eqs. (i) and (ii), we get
$r=3(2r+3q)+4q$
$r=6r+9q+4q$
$\Rightarrow 5r=-13q$
$\Rightarrow r=-\frac{13}{5}q$
$\therefore r$ and $q$ have opposite directions.
Hence, $|r|>2|q|$