Relationship between vectors perpendicular to a given vector

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Let vectors $a=a_1i+a_2j+a_3k$ $b=b_1i+b_2j+b_3k$ $c=c_1i+c_2j+c_3k$ be such that $a\cdot b=0$ and $a\cdot c=0 $ Then how are vectors b and c related mathematicaly