Question

If A=(6i-8j) units, B=(-8i-3j) units, and C=(26i-19j) units, determine a and b such that aA+bB+C=0

Answer 1

Given:

$A=6i-8j;\\ B=-8i-3j;\\ C=26i-19j.$

$$aA+bB+C=a(6i-8j)+b(-8i-3j)+26i-19j=0$$

$$\begin{matrix} 6a-8b & =&-26 \\ -8a-3b & =& 19 \end{matrix}$$

Roots

$$a=-\frac{115}{41},\quad b=\frac{47}{41}$$