Perpendicular Lines

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Two lines with direction ratios (a₁, b₁, c₁) and (a₂, b₂, c₂) are perpendicular if

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1. **Theory**: Two lines are perpendicular if the angle $	heta$ between them is $90^\circ$, which means $\cos 90^\circ = 0$.
2. **Calculation**: Using the direction ratio vectors $\vec{v_1} = (a_1, b_1, c_1)$ and $\vec{v_2} = (a_2, b_2, c_2)$.
3. **Condition**: $\vec{v_1} \cdot \vec{v_2} = 0 \iff a_1a_2 + b_1b_2 + c_1c_2 = 0$.

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Perpendicular Lines

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