Calculus

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Where does the line [x, y, z] = [6, 10, 1] + t[3, 4, -1] meet the xy-plane?

  • Calculus -

    The x-y plane is where z=0.
    So solve the equation of the line where z=0, i.e.
    z=1+t[-1]=0
    =>
    t=1
    Substitute t=1 into
    [x, y, z] = [6, 10, 1] + t[3, 4, -1]
    gives
    [x,y,z]=[6,10,1]+1[3,4,-1]=[9,14,0]

  • Calculus -

    So the final answer for this one would be
    [x,y,z]=[6,10,1]+1[3,4,-1]=[9,14,0] ?

    Thank you!

  • Calculus -

    Right.
    You're welcome!

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