Question

$\overline{A}=6.00\hat{i}-8.00\hat{j}$ units, $\overline{B}=8.00\hat{i}+3.00\hat{j}$units and $\overline{C}=26.0\hat{i}+19.0\hat{j}$ units. lf $a\overline{A}+b\overline{B}+\overline{C}=0$, the values of $a$ and $b$ are

• A. $\frac{111}{123}and\frac{-161}{41}$
• B. $\frac{-111}{123}and\frac{-161}{41}$
• C. $\frac{111}{123}and\frac{161}{41}$
• D. $\frac{-111}{123}and\frac{161}{41}$

Answer 1

The correct option is A $\frac{111}{123}and\frac{-161}{41}$

Equating the components of $\hat{i}$ and $\hat{j}$ we get:

$6a+8b+26=0$
$-8a+3b+19=0$

Solving these 2 equations we get:
Values of $a$ and $b$ are $\frac{111}{123}$ and $\frac{-161}{41}$.