I am in Calculus three and we have at a lot of problems that ask for parametric equations, and normal/binormal vectors at a given point. They always give me a point (1, 2/3, 1) and the solutions use t=1. How do you know and find the value you use for t in these problems?
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The form of a parametric equation is always x=x' + at, y= y'+bt, z=z'+ ct. So when they give you the point, they are giving you the values to use for x',y', and z'. So here, your x'=1, y'=2/3, and z'=1. The a,b, and c are constants given to you in the equations. From there, you can use any value of t that you would like to find other points to find normal vectors and lots more fun stuff. The simplest one to use is usually t=1, which is why the book would tell you to do that. But you could also do t=2, t=-357, or any number that you like.
Hope that helps!
Hope that helps!