Linear Algebra: A Modern Introduction

All vectors in the form of \begin{bmatrix} x \\ -3x \\ \end{bmatrix} $x \in \mathbb{R}$
We know that two vectors are orthogonal if their dot product is $0$. Hence: $u\cdot v=0\\x\cdot3+y\cdot1=0\\3x+y=0\\y=-3x$ So all vectors in the form of \begin{bmatrix} x \\ -3x \\ \end{bmatrix} where $x \in \mathbb{R}$ will be orthogonal to $u$