Chapter 5 - Inner Product Spaces - 5.1 Length and Dot Product in Rn - 5.1 Exercises - Page 236: 81

$u\cdot (cv+dw)=0$.

Since $u$ is orthogonal to $v$ and $w$, then we get $$u\cdot v=0, \quad u\cdot w=0.$$ Keeping this in mind, now, \begin{align*} u\cdot (cv+dw)&=c (u\cdot v)+d (u\cdot w)\\ &=0+0\\ &=0. \end{align*} Hence, $u$ is orthogonal to $cv+dw$.