Calculus

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Which plane goes through the origin and is perpendicular to the line r=(2,-2,1) + s(2,3,-4), seR?

a) 2x-2y+z=0
b) 2x+3y-4z=0
c) 2x+3y+z-4=0

d) none of the above.

I got D, none of the above. I have substituted and couldn't find the answer equal to zero.

  • Calculus -

    1.
    The line has direction numbers (2,3,-4)

    The direction numbers of the normal of plane b)
    are (2,3, -4)

    Since the normal is perpendicular to the plane
    the given line is perpendicular to the plane

    2.
    Does (0,0,0 satisfy the equation of plane b) ?
    LS = 2(0) + 3(0) - 4(0) = 0
    RS = 0 , so YES, it does

    your correct answer is b)

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