(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that every point on the line v = (1,-1,2) + t(2,3,1) satisfies the equation

5x - 3y - z - 6 = 0

2. Relevant equations

3. The attempt at a solution

So what I did was solve the equation v by adding the x,z,and z components to get

x = 1 + 2t

y = -1 + 3t

z = 2 + t

So I'm thinking that if I can combine these into one equation that I would end up getting the answer. Problem is I can't figure out how to combine the three equations in an equation with all three variables. I keep getting the function in terms of two variables, or the wrong answer all together. One method I used was solving the z equation for t and then plugging it into the x equation and then the y equation. I tried setting they both equal to zero...

t = z -2

y = 3z-7 y - 3z + 7 = 0

x = 2z-3 x - 2z + 3 = 0

y - 3z + 7 = x -2z + 3

y - z - x + 4 = 0

Obviously this isn't the correct answer. What am I doin' wrong here?

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# Homework Help: Combining Parametric Equations

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