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The line of greatest slope on an incline...

The line of greatest slope on an inclined plane `P_1` is that line in the plane which is perpendicular to the line of intersection of plane `P_1` and a horiontal plane `P_2`.
Q. Assuming the plane `4x-3y+7z=0` to be horizontal, the direction cosines of line greatest slope in the plane `2x+y-5z=0` are

A

`(3)/(sqrt(11)), -(1)/(sqrt(11)), (1)/(sqrt(11))`

B

`(3)/(sqrt(11)), (1)/(sqrt(11)), -(1)/(sqrt(11))`

C

`-(3)/(sqrt(11)), (1)/(sqrt(11)), (1)/(sqrt(11))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
(a)
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Knowledge Check

  • The direction of the line of instersection of the planes 3x-z = 5 and 2y + x+z = 3 is ....

    A
    (2,-4,6)
    B
    (1,-2,3)
    C
    (-1,2,3)
    D
    (1,-2,-3)

  • Out of the following planes , which plane is passing through theline of intersection of the palnes x-y+2z = 3 and 4x-3y-z = 1.

    A
    11x + 10 y -5z=0
    B
    7x+7y+4z = 0
    C
    5x+2y-z = 2
    D
    None to these

  • The plane 2x - (1- lambda) y+ 3 lambda z= 0 is passing through the line of intersectoin of ...... Planes.

    A
    `2x-y = 0 , y-3z = 0`
    B
    `2x-y + 3z = 0 ,y=0`
    C
    `2x-y+3z = 0,y - 3z = 0`
    D
    None of these

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    Find the equation of the plane which is perpendicular to the plane 5x + 3y + 6z + 8 = 0 and which contains the line of intersection of the planes x + 2y + 3z - 4 = 0 and 2x + y - z + 5 = 0.

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