Statement 1 - If the planes x = cy + b z , y = a z + c x and z = b x + a y pass through a line, then a 2 + b 2 + c 2 + 2 ab c = 1 . Statement 2 - The determinant with rows ( 1 , − c , − b ) , ( − c ,

Question

Statement 1 - If the planes x = cy + b z , y = a z + c x and z = b x + a y pass through a line, then a 2 + b 2 + c 2 + 2 ab c = 1 . Statement 2 - The determinant with rows ( 1 , − c , − b ) , ( − c , 1 , − a ) , ( − b , − a , 1 ) is equal to 0 .

TestHub · Accepted Answer

Three homogeneous planes through the origin pass through a common line when the determinant of coefficients is zero. Expanding: 1 − a 2 − b 2 − c 2 − 2 ab c = 0 . So Statement 2 is true and gives Statement 1.

Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

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