Thread: Find the Unit Vector View Single Post
Math
Emeritus
dy/dx is the ratio of the y-component of the tangent vector to the x-component. Coupling that with the requirement that the length be 1 lets you determine both. For example, if dy/dt= vy/vx= 2 then vy= 2vx. If then $\sqrt{v_x^2+ v_y^2}= 1$, we have vx2+ vy2= vx2+ 4vx2= 5v[sup]x[/sub]2= 5 so $v_x= 1/\sqrt{5}$ and $v_y= 2/\sqrt{5}$.