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Assuming the plane to be horizontal
MATHEMATICS · Single correct · ISC · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry
Problem Assuming the plane 4 x − 3 y + 7 z = 0 4x - 3y + 7z = 0 4 x − 3 y + 7 z = 0 to be horizontal, the direction cosines of the line of greatest slope in the plane 2 x + y − 5 z = 0 2x + y - 5z = 0 2 x + y − 5 z = 0 are
(1) ( 3 11 , − 1 11 , 1 11 ) \left(\frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}}, \frac{1}{\sqrt{11}}\right) ( 11 3 , 11 − 1 , 11 1 )
(2) ( 3 11 , 1 11 , − 1 11 ) \left(\frac{3}{\sqrt{11}}, \frac{1}{\sqrt{11}}, \frac{-1}{\sqrt{11}}\right) ( 11 3 , 11 1 , 11 − 1 )
(3) ( − 3 11 , 1 11 , 1 11 ) \left(\frac{-3}{\sqrt{11}}, \frac{1}{\sqrt{11}}, \frac{1}{\sqrt{11}}\right) ( 11 − 3 , 11 1 , 11 1 )
(4) ( 1 11 , 3 11 , − 1 11 ) \left(\frac{1}{\sqrt{11}}, \frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}}\right) ( 11 1 , 11 3 , 11 − 1 )
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