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4.2 Vector Algebra: ) eth 08 Veetor addition: any two vectors a = (ay,a) and b = (b,,b2) ae have i EHF = (ar, a) + (by, be) = (ay + by, a2 + bg) a etrically, consider two vectors d = (a,, a2) dB = (yb). a third vector 2 (c,,¢,) can te formed by placing the initial point of B on the - point of @ and then joining the initial Nt int of @ to the terminal of B as shown B ea é fe three vectors @ and B and @ therefore form sides of a triangle ABC. @ is said to be the ined by using the triangle law. The triangle Law of Addition: Fhe triangle law states that, the sum of the ors @ and b is given by @ where ABC is a ied =G+B efinition2.1.1.2: Two vectors are collinear if ey lie on the same line. $ $ B ¢ en the addition gives the sum of the ignitude and the direction remains the same e é¢=a+5 finition2.1.1.3 (Negative Vector): Suppose 4 db have the same magnitude but opposite in direction i.e. A and C Coincide a d+ b=AB+BC= AC ie. AB+ BC=0 Since A. coincide with C. This means the sum of two unlike vectors but of the same magnitude is the zero vector (or null vector). B= —BA or BA=~—AB and AB +(-AB) = We shall now define the negative vector of @ as that vector —d having the same magnitude and direction as @ but of opposite sense. Since by definition AB = BA we have —(-BA) = BA. Note: The sum of two vectors @ and 6 can again be obtained by completing the parallelogram formed by the two vectors c) The Parallelogram Law of Addition: The parallelogram law of vector addition states that the sum of two vectors dand & is given by ¢ where OACB isa parallelogram. Consider the parallelogram below. A b Cc d) The Polygon Law: The addition of three of more vectors can bé done by a fepeated application of the trianglé law. The sum of these vectors then completes a polygon formed by the vectors. This is called polygon law‘of vector addition. For example, given below are the vectors Page 41 
