IGCSE›Edexcel IGCSE Maths›Mind mapsVectorsEdexcel IGCSE Maths: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsWhat is a vector?Has magnitude and directionColumn vector: horizontal over verticalAB⃗\vec{AB}AB means from AAA to BBBAB⃗=−BA⃗\vec{AB} = -\vec{BA}AB=−BAParallel if one is a scalar multipleVector arithmeticAdd and subtract component-wiseka⃗k\vec{a}ka multiplies every componentNegative kkk reverses direction2a⃗−b⃗2\vec{a} - \vec{b}2a−b with a⃗=(4,−1)\vec{a}=(4,-1)a=(4,−1), b⃗=(−2,3)\vec{b}=(-2,3)b=(−2,3)Answer: (10,−5)(10,-5)(10,−5)Vectorsmagnitude and directionAB⃗\vec{AB}ABa\mathbf{a}aMagnitudeUse Pythagoras∣a⃗∣=x2+y2|\vec{a}| = \sqrt{x^2 + y^2}∣a∣=x2+y2Always positive, no direction(6,−8)(6,-8)(6,−8) → 36+64=\sqrt{36+64} = 36+64= 10Position vectorsOA⃗\vec{OA}OA locates AAA from origin OOOAB⃗=b⃗−a⃗\vec{AB} = \vec{b} - \vec{a}AB=b−aEnd minus startMidpoint: 12(a⃗+b⃗)\tfrac{1}{2}(\vec{a}+\vec{b})21(a+b)Ratio m:nm:nm:n: a⃗+mm+n(b⃗−a⃗)\vec{a} + \frac{m}{m+n}(\vec{b}-\vec{a})a+m+nm(b−a)ProofsWrite vectors using the base vectorsShow AB⃗=kBC⃗\vec{AB} = k\vec{BC}AB=kBC for parallelCollinear needs a shared point tooParallel alone is not enough for collinear