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CSCA MathematicsChapter 3: Geometry & AlgebraBeginner

Plane Vectors: Linear Operations & Dot Product

平面向量的线性运算与数量积 · Node 3.2

Vector coordinates, collinearity condition $x_1 y_2 - x_2 y_1 = 0$, dot product $\mathbf{a}\cdot\mathbf{b}$, angle formula, and orthogonality.

Chapter Weight: 25% of official examination
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Core Mathematical Axiom

Formula Proof & Traps
a⋅b=∣a∣∣b∣cosθ=x1​x2​+y1​y2​,a⊥b⟺x1​x2​+y1​y2​=0
CSCA Exam Trap Alert

Confusing parallel vector condition $(x_1 y_2 - x_2 y_1 = 0)$ with perpendicular condition $(x_1 x_2 + y_1 y_2 = 0)$.

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