IGCSE›Cambridge IGCSE Maths›Mind mapsVectorsCambridge IGCSE Maths: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsWhat is a vector?Has magnitude and directionColumn vector (xy)\binom{x}{y}(yx): xxx across, yyy upAB→\overrightarrow{AB}AB is the vector from A to BPrinted in bold, e.g. a\mathbf{a}aVector arithmeticAdd or subtract component by component(23)+(1−4)=(3−1)\binom{2}{3} + \binom{1}{-4} = \binom{3}{-1}(32)+(−41)=(−13)Scalar multiple: 3(2−1)=(6−3)3\binom{2}{-1} = \binom{6}{-3}3(−12)=(−36)Scalar multiples are parallel to the originalNegative scalar reverses directionVectorssize and direction(xy)\binom{x}{y}(yx)AB⃗\vec{AB}ABMagnitudeLength of (xy)\binom{x}{y}(yx) is x2+y2\sqrt{x^2 + y^2}x2+y2Uses Pythagoras(34)\binom{3}{4}(43) has magnitude 25=\sqrt{25} =25= 5Position vectorsOA→\overrightarrow{OA}OA gives the position of A from origin OAB→=OB→−OA→\overrightarrow{AB} = \overrightarrow{OB} - \overrightarrow{OA}AB=OB−OATrace a route between points using given vectorsWith the arrow: add, against it: subtractProof and tipsParallel lines: one vector is a scalar multiple of the otherCollinear points need parallel vectors and a common pointParallel alone does not prove collinear