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 | 1 | initial version | posted 2014-07-11 09:08:08 -0600  |
To solve the system of equations $u_{1}^{2}+u_{2}^{2}=1$ and $2u_{1}+u_{2}=1$.
think of them as a circle $x^{2}+y^{2}=1$ and a line $y=-2x+1$ and plug in the equation of the line for $y$ in the circle equation. This leaves you with $$(-2x+1)^2+x^2=1$$.
When you foil out the polynomial you get $$5x^2-4x=0$$ $$\longrightarrow x(5x-4)=0$$
The solutions to this equation provide the intersections of the line and circle described earlier which are you can use to construct the appropriate unit vectors.
| | 2 | No.2 Revision |
To solve the system of equations $u_{1}^{2}+u_{2}^{2}=1$ and $2u_{1}+u_{2}=1$.
think of them as a circle $x^{2}+y^{2}=1$ and a line $y=-2x+1$ and plug in the equation of the line for $y$ in the circle equation. This leaves you with $$(-2x+1)^2+x^2=1$$.
When you foil out the polynomial you get $$5x^2-4x=0$$ $$\longrightarrow x(5x-4)=0$$
$x=0$ and $x=\frac{4}{5}$ are the solutions.
The solutions to this equation provide the intersections of the line and circle described earlier which are you can use to construct the appropriate unit vectors.
