SOLUTION: find the equation of a line passing through (2,-1,3) and is orthogonal to 3x-7y+5z+55=0, where does the line intersect the plane

Question 1026390: find the equation of a line passing through (2,-1,3) and is orthogonal to 3x-7y+5z+55=0, where does the line intersect the plane
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
The normal vector defining the equation of the plane is {3, -7, 5}.
Let (x,y,z) be a point on the desired line. Then combined with the given point (2,-1,3) the vector {x-2, y+1, z-3} must be parallel to the vector {3, -7, 5}.
Hence {x-2, y+1, z-3} = k{3, -7, 5}
==> the symmetric equation would be

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