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In each of the following cases, determin...

In each of the following cases, determine the direction cosines of the normal to the plane and the distance from the origin.
(a) z=2
(b) x+y+z=1
(c) 2x+3y-z=5
(b) 5y+8=0

Text Solution

Verified by Experts

The correct Answer is:
(a) =2
(b) `=(1)/(sqrt3)`
(c) `=(5)/(sqrt(14))`
(d) `=8/5`
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Knowledge Check

  • The coordinates of the foot of the perpendicular drawn from the origin to the plane 2x -3y +4z -6=0 are ……

    A
    `((12)/(29),(-18)/(29),(24)/(29))`
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  • The coordinates of the foot of the perpendicular drawn from the origin to the plane 2x -3y +4z -6=0 are ……

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    `((12)/(29),(-18)/(29),(24)/(29))`
    B
    `((12)/(sqrt(29)),(-18)/(sqrt(29)) ,(24 )/( sqrt(29)))`
    C
    `((6)/(29 ),(-9)/(29 ),(12)/(29))`
    D
    `((6)/(sqrt(29)),(-9)/(sqrt(29)) , (12)/(sqrt(29)))`

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