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State True or False. There exist four distinct points $$A$$, $$B$$, $$C$$, $$D$$ in a plane such that $$\overleftrightarrow{AD} \perp \overleftrightarrow{BC}$$ and $$\overleftrightarrow{BD} \perp \overleftrightarrow{CA}$$.
Correct Answer: True
Take any triangle $$ABC$$ without a right angle and let $$D$$ be its orthocentre. Then $$AD$$ and $$BD$$ lie along altitudes, so $$AD \perp BC$$ and $$BD \perp CA$$, and $$D$$ is different from $$A$$, $$B$$, $$C$$. Such points exist, so the statement is True.
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