- #1
gnome
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I'm trying to finish a geometrical argument (the full details will only confuse matters) and I'm down to a final (crucial) point for which I can't think of a convincing proof.
Suppose we have two planes: plane A formed by connecting points vwx and plane B formed by connecting points wxy, so line wx lies along the intersection of plane A with plane B. Now I add another plane C which is orthogonal to both A and B and also passes through points v and y. I want to say that the LINE formed by the intersection of plane C with plane B is orthogonal to line wx.
Sorry I can't provide a picture of this, but it may help to visualize a pyramid with a triangular base; the three base vertices are at w, x and y, and the apex is at v. Plane B is the base, A is the side formed by v,w and x, and C slices vertically through the pyramid along line vy.
I'm pretty sure that the line formed by C's intersection with B coincides with the altitude (along the base) from vertex y to edge wx, but I can't quite convince myself.
Edit: picture is attached to post #4
Suppose we have two planes: plane A formed by connecting points vwx and plane B formed by connecting points wxy, so line wx lies along the intersection of plane A with plane B. Now I add another plane C which is orthogonal to both A and B and also passes through points v and y. I want to say that the LINE formed by the intersection of plane C with plane B is orthogonal to line wx.
Sorry I can't provide a picture of this, but it may help to visualize a pyramid with a triangular base; the three base vertices are at w, x and y, and the apex is at v. Plane B is the base, A is the side formed by v,w and x, and C slices vertically through the pyramid along line vy.
I'm pretty sure that the line formed by C's intersection with B coincides with the altitude (along the base) from vertex y to edge wx, but I can't quite convince myself.
Edit: picture is attached to post #4
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