Two systems of rectangular axes have same origin. If a plane cuts them at distances \( a, b, c \... VIDEO
Two systems of rectangular axes have same origin. If a plane cuts them at distances \( a, b, c \) and \( a_{1}, b_{1}, c_{1} \) from
\( \mathrm{P} \) the origin, then
W
(1) \( \frac{1}{\mathrm{a}^{2}}+\frac{1}{\mathrm{~b}^{2}}+\frac{1}{\mathrm{c}^{2}}=\frac{1}{\mathrm{a}_{1}^{2}}+\frac{1}{\mathrm{~b}_{1}^{2}}+\frac{1}{\mathrm{c}_{1}^{2}} \)
(2) \( \frac{1}{a^{2}}-\frac{1}{b^{2}}+\frac{1}{c^{2}}=\frac{1}{a_{1}^{2}}-\frac{1}{b_{1}^{2}}+\frac{1}{c_{1}^{2}} \)
(3) \( a^{2}+b^{2}+c^{2}=a_{1}^{2}+b_{1}^{2}+c_{1}^{2} \)
(4) \( a^{2}-b^{2}+c^{2}=a_{1}^{2}+b_{1}^{2}+c_{1}^{2} \)
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