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M Quack
M Quack is offline
#17
Apr2-12, 03:12 PM
P: 640
Oh well.. :-)

Let [itex]\vec{a}=\left(\begin{array}{c}0\\ 0\\1 \end{array} \right)[/itex]

Let [itex]C_3 = \left( \begin{array}{ccc} c & -s & 0 \\ s & c & 0\\ 0 & 0 & 1 \end{array} \right) [/itex]

With s=sin(120 deg) and c= cos(120 deg).

Calculate [itex] \vec{b} = C_3 \vec{a} [/itex] and [itex] \vec{d} = C_3 \vec{b} [/itex]

Write d as linear combination of a and b.

Show C_3^3 =1 and C_3 c = c with c=(0 0 1)