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MATH 53 (3)
Midterm

# Midterm 1 Review - 10/11/13 Lecture Notes

2 Pages
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Department
Mathematics
Course Code
MATH 53
Professor
Denis Auroux

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Description
Midterm Review β October 11, 2013 Topics: Everything Vectors & Geometry Dot Product πβ β π = β π π = π |β οΏ½ποΏ½cosπ π π Finding angles, components, detecting β₯ Determinants (2d, 3d= π β β (π Γ β)) οΏ½ π€Μ π₯Μ π Cross Product πβ Γ π = οΏ½ π1 π 2 π 3οΏ½ π1 π2 π 3 Direction β₯ π β, π Length= Area of parallelogram formed byπ β, π Equations of planes ππ₯ + ππ¦ + ππ§ = π, < π,π,π >= normal vector Equations of lines π₯ = π₯ 0 ππ‘ Parametric equationοΏ½ π¦ = π¦ 0 + ππ‘ , < π,π,π > β₯ to the line π§ = π§ + ππ‘ < π₯ 0π¦ 0π§ >0is point on line 0 (Symmetric equations) Geometry of lines and planes (Intersections, angles, distances(see Figure 1)) Ex. Plane through A (0, 1, 2), B (2, -1, 3), C (1, 0, 1) π΄π΅ =< 2,β2,1 > π΄πΆ =< 1,β1,β1 > π€Μ π₯Μ π οΏ½β = π΄π΅ Γ π΄πΆ = οΏ½β οΏ½ =< 2 + 1,β β2 β 1 ,β2 + 2 >=< 3,3,0 > 2 β2 1 1 β1 β1 3π₯ + 3π¦ + 0π§ = 3 0 + 3 1 + 0 2 = 3 or π₯ + π¦ = 1 Parametric curves (split between Chapters 10 & 13) Finding parametric equations geometrically Velocityπ£ β = ππ, Acceleration πβ = ππ£β ππ‘ ππ‘ Speed = π£|β , Unit Tangent π = π£β π£β| Arc Length π
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