Let $x$ and $y$ be real numbers such that $x^2 + y^2 = 1$. Find the maximum value of $2x – 5y$.
I do know how to solve this problem using trigonometry, however I need to solve it by using vectors. Except for defining vector $v=(x, y)$, such that $||v||=1$, I do not see any way in which I could apply vectors to solving this problem. Any ideas are appreciated. Thank you!
Best Answer
Let $\vec a=(2,-5), \vec b=(x,y)$.
$2x-5y=\vec a\cdot \vec b=\sqrt{2^2+(-5)^2}\cdot\sqrt{x^2+y^2}\cos\theta\le\sqrt{29}$ where $\theta$ is the angle between the two vectors.