M35 · Overview Vectors mind map

Use your browser’s Print command for A4 landscape, or choose A3 in its paper settings. The SVG remains sharp when enlarged. A text version follows the map.

M35 · Overview Vectors mind map

Read the mind map as text

Vectors

Components: Magnitude and direction; equal components, different positions
Length: Magnitude √(x²+y²); (3,4) has length 5

Arithmetic

Add / subtract: Component by component; head-to-tail; subtraction reverses
Scalar: Scales length; negative reverses direction

Positions

Direction: Higher: AB=B−A; if OA=a,OB=b then AB=b−a
Routes: Higher: AB+BC=AC; keep arrow start/end labels consistent

Proof / ratios

Divide: Higher: Midpoint (a+b)/2; ratio1:2 from A → a+(b−a)/3
Parallel / collinear: Higher: Non-zero scalar multiples; collinear shares common point
Intersection: Higher: Use two routes; equate independent vector coefficients

Connections

Arithmetic → Positions: Component arithmetic agrees with directed routes
Positions → Proof / ratios: Scalar multiples prove parallel relationships