Question

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are non-collinear vectors and $A=(p+4q)a+(2p+q+1)b$
$B=(-2p+q+2)a+(2p-3q-1)b$ then determine $p$ and $q$, so that $3A=2B.$

• A. $p=1$ and $q=-0.3$
• B. $p=-1$ and $q=1.1$
• C. $p=2$ and $q=-1$
• D. $p=-2$ and $q=1.8$

Answer 1

The correct option is C $p=2$ and $q=-1$

Substitute the values of $A$ and $B$ and then equating the coefficients of a and b on both sides, we get
$3(p+4q)=2(-2p+q+2)$
and $3(2p+q+1)=2(2p-3q-1)b$
or $7p+10q=4$ and $2p+9q=-5.$
Solving these, we get $p=2$ and $q=-1.$