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? asked in 科學數學 · 1 decade ago

線性代數,投影求交點

find the point of intersection with the plane whose equation is x - 3y + 2z = 4

[x y z] = [1 -2 3] + t[2 5 -1]

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  • 1 decade ago
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    find the point of intersection with the

    plane whose equation is x-3y + 2z = 4

    [x y z] = [1 -2 3] + t[2 5 -1]

    Sol

    [x y z] = [1 -2 3] + t[2 5 -1]=[2t+1 5t-2 -t+3]

    x-3y+2z=4

    (2t+1)-3(5t-2)+2(-t+3)=4

    2t+1-15t+6-2t+6=4

    -15t+13=4

    15t=9

    t=3/5

    (x,y,z)=(2*3/5+1,5*3/5-2,-3/5+3)=(11/5,1,12/5)

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