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Analytic Geometry2D

Vector Analytic Geometry - Theory & Concepts - Vector Resolution3 D

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

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3D Vector Configuration

Adjust the magnitude and two coordinate direction angles. The third angle (γ\gamma) is calculated automatically to satisfy the identity cos⁡2α+cos⁡2β+cos⁡2γ=1\cos^2\alpha + \cos^2\beta + \cos^2\gamma = 1.

100 N
60°
60°
Calculated Angle γ (from z-axis):
γ≈45.0∘\gamma \approx 45.0^\circ

Rectangular Components

X - Component (FxF_x)+50.0 N
Y - Component (FyF_y)+50.0 N
Z - Component (FzF_z)+70.7 N
Cartesian Vector Formulation
F={50.0i+50.0j+70.7k} N\mathbf{F} = \{50.0\mathbf{i} + 50.0\mathbf{j} + 70.7\mathbf{k}\}\text{ N}

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