Assuming the plane to be horizontal

MATHEMATICS · Single correct · ISC · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

Assuming the plane 4x−3y+7z=04x - 3y + 7z = 0 to be horizontal, the direction cosines of the line of greatest slope in the plane 2x+y−5z=02x + y - 5z = 0 are (1) (311,−111,111)\left(\frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}}, \frac{1}{\sqrt{11}}\right) (2) (311,111,−111)\left(\frac{3}{\sqrt{11}}, \frac{1}{\sqrt{11}}, \frac{-1}{\sqrt{11}}\right) (3) (−311,111,111)\left(\frac{-3}{\sqrt{11}}, \frac{1}{\sqrt{11}}, \frac{1}{\sqrt{11}}\right) (4) (111,311,−111)\left(\frac{1}{\sqrt{11}}, \frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}}\right)

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