Let a, b, c be non-zero vectors. Explain geometrically why the equation a×b=a×c does not necessarily imply that b = c. If a × b = a × c and a · b = a · c, would it follow that b = c?
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HINT: Consider the vectors $\displaystyle A=\left\langle {1,2,3} \right\rangle ,B=\left\langle {2,4,6} \right\rangle ,C=\left\langle { - 1, - 2, - 3} \right\rangle$.
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