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MATHEMATICS · Single correct · CBSE · Mathematics · Three-Dimensional Geometry · ISC
Problem A plane cutting the axes in P , Q , R P, Q, R P , Q , R ( α − β , β − γ , γ − α ) (\alpha - \beta, \beta - \gamma, \gamma - \alpha) ( α − β , β − γ , γ − α ) O O O O P Q R OPQR O P QR α x + β y + γ z = 4 \alpha x + \beta y + \gamma z = 4 α x + β y + γ z = 4 ( α − β ) x + ( β − γ ) y + ( γ − α ) z = 0 (\alpha - \beta)x + (\beta - \gamma)y + (\gamma - \alpha)z = 0 ( α − β ) x + ( β − γ ) y + ( γ − α ) z = 0 ( α − β ) y z + ( β − γ ) z x + ( γ − α ) x y = 2 x y z (\alpha - \beta)yz + (\beta - \gamma)zx + (\gamma - \alpha)xy = 2xyz ( α − β ) y z + ( β − γ ) z x + ( γ − α ) x y = 2 x y z ( 1 α 2 + 1 β 2 + 1 γ 2 ) ( x 2 + y 2 + z 2 ) = x y z \left(\frac{1}{\alpha^2} + \frac{1}{\beta^2} + \frac{1}{\gamma^2}\right)(x^2 + y^2 + z^2) = xyz ( α 2 1 + β 2 1 + γ 2 1 ) ( x 2 + y 2 + z 2 ) = x y z Browse the problem library