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Vector Equations

  • 03-01-2013 07:25PM
    #1
    Pudsy33
    Registered Users, Registered Users 2 Posts: 10,910 ✭✭✭✭


    I have 2 vector equations

    v=(0,-3,1)+t(2,-2,4)

    w=(-1,-2,-1)+u(-1,1,-2)

    how can I verify these describe the same line?

    I know from an earlier question (-1,-2,-1) is also on the first line

    Thanks


Comments

  • #2
    sponsoredwalk
    Registered Users, Registered Users 2 Posts: 3,038 ✭✭✭sponsoredwalk


    Think of the geometry of what v= (0,-3,1) + t(2,-2,4) is saying, since t(2,-2,4) is in the equation with t as a variable it's saying that you're getting all multiples of the vector (2,-2,4), which describes a line in space. Thus you can think of the vector (2,-2,4) as describing the direction of the line. So what does the vector (0,-3,1) mean? If t = 0 then you're just at the point (0,-3,1), if t = 1 then you're at (0,-3,1) + (2,-2,4) etc... So if t was only positive you'd have a line starting from the point (0,-3,1) & going off in the direction that (2,-2,4) points in, thus the vector (0,-3,1) is a way to say that we're shifting a line through the origin to a line through the point (0,-3,1). So now what would the conditions be for w = (-1,-2,-1) + u(-1,1,-2) to describe the same line?
    What would (-1,-2,-1) have to satisfy?
    What would (-1,1,-2) have to satisfy?


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