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Let the points \( \mathrm{A}(\mathrm{a}, \mathrm{b}, \mathrm{c}) \) and \( \mathrm{B}\left(\mathrm{a}^{\prime}, \mathrm{b}^{\prime}, \mathrm{c}^{\prime}\right) \) be at distances \( r \) and \( r^{\prime} \) from origin. The line \( A B \) passes through origin
\( \mathrm{P} \) when

W
(1) \( \frac{\mathrm{a}^{\prime}}{\mathrm{a}}=\frac{\mathrm{b}^{\prime}}{\mathrm{b}}=\frac{\mathrm{c}^{\prime}}{\mathrm{c}} \)
(2) \( a a^{\prime}+b b^{\prime}+c c^{\prime}=r r^{\prime} \)
(3) \( a a^{\prime}+b^{\prime}+c^{\prime}=r^{2}+r^{\prime 2} \) (4) \( \frac{2 a^{\prime}}{\mathrm{a}}=\frac{b^{\prime}}{b}=\frac{2 c^{\prime}}{c} \)
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