## Calculus 8th Edition

$c=\frac{1}{2}a+\frac{1}{2}b$, $d=\frac{1}{2}b-\frac{1}{2}a$
As per parallelogram law: $a+b=2c$ Divide both sides by scalar $2$, we get $c=\frac{a+b}{2}$ $c=\frac{1}{2}a+\frac{1}{2}b$ From the figure we can see that: $a+2d=b$ $2d=b-a$ Divide both sides by scalar $2$, we get $d=\frac{b-a}{2}$ $d=\frac{1}{2}b-\frac{1}{2}a$