Presentation on theme: "Addition of vectors (i) Triangle Rule [For vectors with a common point] C B A."— Presentation transcript:
1 Addition of vectors(i) Triangle Rule [For vectors with a common point]CBA
2 (ii) Parallelogram Rule [for vectors with same initial point] DCBA
3 (iii) Extensions follow to three or more vectors p+q+rqp
4 First we need to understand what is meant by the vector – a SubtractionFirst we need to understand what is meant by the vector – aa– aa and – a are vectors of the same magnitude, are parallel, but act in opposite senses.
8 OP is a position vector of a point P. We usually associate p with OP Position VectorsRelative to a fixed point O [origin] the position of a Point P in space is uniquely determined by OPPpOP is a position vector of a point P. We usually associate p with OPO
11 Vectors Questions P A a N O b B Q Example In the diagram, OA = AP and BQ = 3OB.N is the midpoint of PQ.andAPNQOBabExpress each of the following vectors in terms of a, b or a and b.(a) (b) (c) (d)(e) (f) (g) (h)
13 ExampleABCDEF is a regular hexagon with , representing the vector m and , representing the vector n. Find the vector representingmABCDFEnm+nm
14 Example M, N, P and Q are the mid-points of OA, OB, AC and BC. OA = a, OB = b, OC = c(a) Find, in terms of a, b and c expressions for(i) BC (ii) NQ (iii) MP(b) What can you deduce about the quadrilateral MNQP?a)BC = BO + OC= c – b(ii) NQ = NB + BQb= ca(ii) MP = MA + APc= cMNPQ is a parallelogram as NQ and MP are equal and parallel.
15 ExampleIn the diagram, and , OC = CA, OB = BE and BD : DA has ratio 1 : 2.a) Express in terms of a and b(i)b) Explain why points C, D and E lie on a straight line.ODBCEAba
16 ExampleABC is a triangle with D the midpoint of BC and E a point on AC such that AE : EC = 2 : 1. Prove that the sum of the vectors , , is parallel to