Vectors in 2D

Description

This animation introduces 2D vectors through visual demonstrations on a number plane. It shows a vector as an arrow, demonstrates scalar multiplication (stretching/shrinking), and vector addition using the tip-to-tail method. Component form and magnitude formula are displayed with MathTex.

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Phases

#	Phase Name	Duration	Description
1	Introduction	5s	NumberPlane appears; single vector v = (2, 1) drawn as arrow
2	Component form	5s	Show (vx, vy) components: horizontal and vertical dashed lines
3	Magnitude	5s	Draw right triangle showing
4	Scalar multiplication	10s	Animate k*v for k = 2 (double), then k = -1 (reverse), then k = 0.5
5	Vector addition	12s	Show vectors u and v; tip-to-tail addition; resultant w = u+v
6	Summary	7s	All formulas visible; final labeled diagram

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Layout

+-----------------------------------------------+
|  v = (vx, vy)           [formula top-right]   |
|  |v| = sqrt(vx²+vy²)                          |
|                                                |
|    ^      ↗ v                                 |
|    |    /   (arrow)                            |
|    |   /                                       |
|    |  /  ← right triangle                     |
|    | /  vx (horiz) vy (vert)                  |
|    +------------>                              |
|                                                |
|  [scalar mult panel]  [addition panel]         |
+-----------------------------------------------+

Area Descriptions

Area	Content	Notes
Center	NumberPlane + vector arrows	Main demonstration area
Top right	Component form + magnitude formulas	MathTex
Bottom	Step labels for each phase	Fade in/out per phase

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Assets & Dependencies

• Fonts: LaTeX
• Colors: V_COLOR = YELLOW, U_COLOR = BLUE, RESULT_COLOR = GREEN, COMPONENT_COLOR = GRAY, BG = #1a1a2e
• Manim version: ManimCE 0.19.1

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Notes

• Use NumberPlane for grid background
• Vectors drawn with Arrow from origin or tip-to-tail
• ValueTracker for scalar k in phase 4
• always_redraw for scaled vector arrow