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Analytic Geometry2D

Vector Analytic Geometry - Theory & Concepts - Analytic Geometry Vector Product

Introduction to vectors, dot product, cross product, and their applications in analytic geometry.

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Vector Dot and Cross Product Visualizer

Manipulate two vectors in 3D space to analyze their dot product, cross product, and spanned parallelogram area

Vector u = ⟨u_x, u_y, u_z⟩
3.0
0.0
3.0
Vector v = ⟨v_x, v_y, v_z⟩
0.0
3.0
2.0
Vector Metrics
Dot Product
6.00
Cross Area
14.07
Angle
66.9°
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u⃗⋅v⃗=(3.0)(0.0)+(0.0)(3.0)+(3.0)(2.0)=6.00\vec{u} \cdot \vec{v} = (3.0)(0.0) + (0.0)(3.0) + (3.0)(2.0) = 6.00
u⃗×v⃗=⟨−9.0,−6.0,9.0⟩,∣u⃗×v⃗∣=14.07\vec{u} \times \vec{v} = \langle -9.0, -6.0, 9.0 \rangle, \quad |\vec{u} \times \vec{v}| = 14.07

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