Two system of rectangular axes have the same origin. If a plane cuts them at distances a_…
Mathematics · JEE Main · NTA Exams — Three Dimensional Geometry
Two system of rectangular axes have the same origin. If a plane cuts them at distances \(a_{1} b_{1} c\) and \(a^{\prime}, b^{\prime}, c^{\prime}\) from the origin, then
- \(\frac{1}{\mathrm{a}^{2}}+\frac{1}{\mathrm{~b}^{2}}+\frac{1}{\mathrm{c}^{2}}+\frac{1}{\mathrm{a}^{12}}+\frac{1}{\mathrm{~b}^{12}}+\frac{1}{\mathrm{c}^{12}}=0\)
- \(\frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}}+\frac{1}{a^{2}}+\frac{1}{b^{\prime 2}}-\frac{1}{c^{\prime 2}}=0\)
- \(\frac{1}{\mathbf{a}^{\mathbf{2}}}-\frac{1}{\mathbf{b}^{\mathbf{2}}}-\frac{1}{\mathbf{c}^{\mathbf{2}}}+\frac{1}{\mathbf{a}^{\mathbf{2}}}-\frac{1}{\mathbf{b}^{\mathbf{2}}}-\frac{1}{\mathbf{c}^{\mathbf{1}^{\mathbf{2}}}}=0\)
- \(\frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}}-\frac{1}{a^{2}}-\frac{1}{b^{\prime 2}}-\frac{1}{c^{\prime 2}}=0\)
Answer
(D) 1 a^ 2 + 1 b^ 2 + 1 c^ 2 - 1 a^ 2 - 1 b^ 2 - 1 c^ 2 =0
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