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Consider the planes 3x-6y-2z=15a n d2x+y...

Consider the planes `3x-6y-2z=15a n d2x+y-2z=5.` Statement 1:The parametric equations of the line intersection of the given planes are `x=3+14 t ,y=2t ,z=15 tdot` Statement 2: The vector `14 hat i+2 hat j+15 hat k` is parallel to the line of intersection of the given planes.

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Explore conceptually related problems

Consider the planes 3x-6y-2z-15=0 and 2x+y-2z-5=0 Statement 1: The parametric equations of the line intersection of the given planes are x=3+14t,y=2t,z=15t .Statement 2: The vector 14hat i+2hat j+15hat k is parallel to the line of intersection of the given planes.

Consider the planes 3x-6y-2z=15 and 2x+y-2z=5 . STATEMENT-1: The parametric equations of the line of intersection of the given planes are x=3+14t, y-1+2t,z=15t . because STATEMENT-2 : The vectors 14i +2j+15k is parallel to the line of intersection of the given planes.

Knowledge Check

  • If t is a parameter, then the line of intersection of the planes 3x-6y-2z=15and2x+y-2z=5 is

    A
    `x=3+14t,y=1+2t,z=15t`
    B
    `x=3+14t,y=-1+2t,z=15t`
    C
    `x=-3+14t,y=1+2t,z=15t`
    D
    none of these

  • A plane P passes through the line of intersection of the planes 2x-y+3z=2,x+y-z=1 and the point (1,0,1). What are the direction ratios of the line of intersection of the given planes ?

    A
    `(: 2,-5,-3 :)`
    B
    `(:1,-5,-3:)`
    C
    `(:2,5,3:)`
    D
    `(:1,3,5:)`

  • A plane P passes through the line of intersection of the planes 2x-y+3z=2.x+y-z=1 and the point (1,0,1) What are the direction ration of the line of intersection of the given planes

    A
    `lt2,-5,-3gt`
    B
    `lt1,-5,-3gt`
    C
    `lt2,5,3gt`
    D
    `lt1,3,5gt`

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    What is the point of intersection of the line x = y = z with the plane x + 2y + 3z = 6 ?

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