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2.5 Multiplication of, We saw that we, vectors of the same type, of the same type. Ho, Vectors of the same or d, @ new physical quantity w E, @ scalar (scalar product) or, Product). Also note that the mi, Scalar with a scalar is always @, multiplication of scalar with a, 4 vector. Let us now study the ©, of a scalar product and vector Pp, vectors., 2.5.1 Scalar Product (Dot Product), \ The scalar product or dot re, nonzero vectors P and @ is defin dith, product of magnitudes of the two vectors and ft, , cosine of the angle @ between the two vectors. ', , The scalar product of P and Q is written, P 0 = PQ cos 8, ] a, , where @ is the angle between PandQ., Characteristics of scalar product :, , @ The scalar product of two vectors is, equivalent to the product of magnitude of bee, vector with the magnitude of the component 0, the other vector in the direction of the first.), , , , 0 Ocos0 Pp P, Fig. 2.9: Projection of vectors,, From Fig. 2.9,, P:Q= PO cos 0, =P(Q cos 0), =P (component of 0 in the direction of P), Similarly P-O = 0(P cos 8), ~2 (component of P in thé direction of 0), ( ea Product obeys the commutative law, of vector multiplication., , P'2=PQc0s0=0 Pcoso=O-p ], , 719s, , distributive lay, , PR, product P.¢ ;, , vectors P and Oo, , roducts are y,, ike mathematicg), n very elegant, , the definition, th,, , is the product of th,., ment in the directioy,, According to the, , = (F cos6) §, product is the, , ‘of one of the vectors, © other vector in the, , of doing work on, force F assumed to, , If v is the velocity of