Inner product/Kernel of 317/Orthonormal basis/Exercise

We endow ${}\mathbb {R} ^{3}$ with the standard inner product. Let ${}U\subseteq \mathbb {R} ^{3}$ be the kernel of the linear mapping

$\mathbb {R} ^{3}\longrightarrow \mathbb {R} ,(x,y,z)\longmapsto 3x+y+7z,$

endowed with the restricted inner product. Determine an orthonormal basis for ${}U$.

Create a solution