Trigonometry 7th Edition

$(a,b)\cdot(-b,a)=a(-b)+b(a)=-ba+ab=0$
If the vectors are perpendicular, their dot product must be zero. Dot product$=(a,b)\cdot(-b,a)=a(-b)+b(a)=-ba+ab=0$ Therefore, $a\textbf {i}+b\textbf {j}$ and $-b\textbf {i}+a\textbf {j}$ will always be perpendicular as long as both $a$ and $b$ are not zero.