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Give the equation of a plane containing the line r = i + 2j + 3k + t(i - j + k) and is parallel to vector v = -i + 2j + 3k.

I'm using this as reference.

My guess is to treat the problem similar to finding an equation of a plane which contains a line and passes through a point. So, I would get a vector on the line (say from t = 0 and t = 1), and a vector from a point on the line (say t = 0) to the vector v (since it is parallel, any multiple of (-1, 2, 3) will suffice). Using these two vectors get the normal, which we can use to derive the equation of the plane.

Is this approach to the solution correct or is there more to it than that? I believe I may be oversimplifying the problem in regards to the parallel vector v.

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# Homework Help: Equation of a plane containing a line and parallel to a vector

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