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Math Help - plane, point, line (vectors)

  1. #1
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    plane, point, line (vectors)

    I was hoping if someone could confirm if those 2 exercises are solved correctly.

    1. we have a plane: (5x-y+z-2=0) and vector line in form: ((t)=x/-2=(y+1)/-3=(z-2)/1). What is the intersection between the two of them?

    What i got is:
    x=-2t
    y=-3t-1
    z=t+2
    5(-2t)-(-3t-1)+t+2-2=0 t=1/6
    x=-1/3
    y=-3/2
    z=13/6

    2.find the perpendicular projection T' of point T(2,-1,5) on vector line : (x-2)/3=(1-z)/2 , y=-3. Also find a point what is a reflection of point T based on the projection T'.

    What i did is:
    s (3,0,-2) = n ( normal of plane that contains point T)
    x=3t + 2
    y=-3
    z=1-2t

    plane: 3x + 0y -2z = d ---> 3*2 -2*5=-4=d
    3x-2z+4=0
    3(3t+2)- 2(1-2t) +4 =0 ---> t = -8/13

    T' (intersection between plane and vector line):
    x= 3t+2=2/13
    y=-3
    z=1-2t=29/13

    to get the point T'' i just calculated the difference between x,y,z coordinates of point T and T' and did the same for coordinates of T' and T'' so i got :
    T''
    x= 2/13 - 24/13 = -22/13
    y= -3 -2 = -5
    z = 29/13 - 36/13 = -7/13
    so i got T'' (-24/13,-5,,-7/13)

    Could this be correct? thank you
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  2. #2
    MHF Contributor
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    Re: plane, point, line (vectors)

    Hey jakobjakob.

    The first one is spot on.

    I'll take a look at the second one in a sec.
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