Two vectors are orthogonal if their dot product is zero. The dot product of two vectors $\mathbf{v}$ and $\mathbf{w}$ is defined as $\mathbf{v} \cdot \mathbf{w}=a_{1} a_{2}+b_{1} b_{2}$, where $\mathbf{v}=a_{1} \mathbf{i}+b_{1} \mathbf{j}$ and $\mathbf{w}=a_{2}
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