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$u$ is orthogonal to $v$ and $w$, that is: $u\cdot v=0$ and $u\cdot w=0$ $u\cdot(cv+dw)=c(u\cdot v)+d(u\cdot w)=c(0)+d(0)=0$ That is, $u$ is also orthogonal to $cv+dw$.
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