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Question: The direction cosines of the normal to the plane \(2 x + 3 y - 6 z = 5\) are...

The direction cosines of the normal to the plane 2x+3y−6z=52 x + 3 y - 6 z = 5 are

A

2,3,−62,3 , - 6

B

27,37,−67\frac { 2 } { 7 } , \frac { 3 } { 7 } , - \frac { 6 } { 7 }

C

25,35,−65\frac { 2 } { 5 } , \frac { 3 } { 5 } , - \frac { 6 } { 5 }

D

None of these

Answer

27,37,−67\frac { 2 } { 7 } , \frac { 3 } { 7 } , - \frac { 6 } { 7 }

Explanation

Solution

Direction ratios of normal to the plane are (2, 3, – 6)

∴\therefore Direction cosines are, (249,349,−649)\left( \frac { 2 } { \sqrt { 49 } } , \frac { 3 } { \sqrt { 49 } } , - \frac { 6 } { \sqrt { 49 } } \right) or (27,37,−67)\left( \frac { 2 } { 7 } , \frac { 3 } { 7 } , \frac { - 6 } { 7 } \right)