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Wednesday
1. Directions
• Through the origin
• Linear independence
• Lines
1. Use vectors to describe the line through points (−1, 2) and (9, −2).
2. Use vectors to describe the line −3x + 4y = 12
3. Use vectors to describe the line −3x + 4y = 8
• Generalized directions
• Parallels
2. Invariants of linear transformations
3. Affine transformations
4. Vector Thales
5. Prove: Diagonals of parallelogram bisect each other
6. Centroid of a triangle:
−−→
(a) Draw a triangle ABC and let N be the midpoint of segment AC. Express BN in
−→
−→
terms of n = AB and m = AC.
−−→
(b) Let M be the midpoint of BC. Write AM in terms of m and n.
−→
−−→
−−→
(c) Express AB + 23 BN in terms of m and n. Express 23 AM in terms of m and n.
Hmmm....
−→ −−→
(d) Let G be the centroid of the triangle ABC. Simplify the vector sum GA + GB +
−→
GC.
7. Inner product
(a) Distance
(b) Orthogonality
(c) Altitudes of any triangle are concurrent
(d) Angle inscribed over a diameter of a circle
(e) Perpendicular bisector
(f) Triangle inequality
(g) Matrix for an isometry
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