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

Find the equation of the plane through the point (-2,8,10) and parallel to the line x= -2+t, y= 1+2t, z= 4-3t.

2. Relevant equations

3. The attempt at a solution

Now, I understand that I have to find the normal vector to the line (and the plane), but how can I do that if I only have one directional vector? If I had another directional vector, I could use the cross product.

I understand that the line has directional vector of (1,2,-3). Is there a way to get the normal vector through this information alone? Maybe by finding the orthogonal vector through the dot product or something (can you do that)?

If I have enough information to find the normal vector, would having only one point on the plane give me enough information to get the equation of the plane?

Thanks for your time, I'm having trouble here.

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# Homework Help: Find a plane given a point and a parallel line

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