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HallsofIvy
HallsofIvy is offline
#4
Sep5-08, 03:57 AM
Math
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Find the Unit Vector


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 [itex]\sqrt{v_x^2+ v_y^2}= 1[/itex], we have vx2+ vy2= vx2+ 4vx2= 5v[sup]x[/sub]2= 5 so [itex]v_x= 1/\sqrt{5}[/itex] and [itex]v_y= 2/\sqrt{5}[/itex].