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Chemical techniques offer a various array of priceless items and fabrics utilized in purposes starting from healthiness care to transportation and foodstuff processing. but those comparable chemical methods that supply items and fabrics necessary to smooth economies, additionally generate monstrous amounts of wastes and emissions.
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Thevector product is defined as: ¯ Definition (see Fig. 1) Vector Analysis 27 axb n I b Fig. 1 Vector Product of TwoVectors where0 is the angle betweena and b, and wheren is normalto the plane of a and b. The sense of n is defined by the "right-hand-role," that is, the direction of advancementof a right hand thread screw, whoseaxis is normalto the plane of a and b, and is turned in the direction of a rotated towardb so as to diminishthe angle between a and h. 4) xz by b If a x b = 0 and if a ~ 0, and b ~ 0, then a is parallel to b.
They may be positive or negative. Frequently appearing scalars in dynamics are time, distance, mass, and force, velocity and acceleration magnitudes. 12 13 Vector Analysis ¯ Multiplication of Scalars and Vectors -- Let D be a scalar and let V be a vector. Then the product sV is a vector with the same orientation and sense as V if s is positive, and with the same orientation but opposite sense of V if s is negative. ) Negative Vector -- The negative of vector V, written as -V, is a vector with the same magnitude and orientation as V, but with opposite sense to that of V.
3 Addition of Vectors -- Geometric Method The sum of two vectors a and b may be obtained by using the parallelogram law (see Fig. 1) or the triangle law (see Fig. 2). The sum of three or vectors may be obtained by using polygon law (see Fig. 2). 1. Then the suma + b is the diagonal of the parallelogram developed by the vectors and passing through the connection point as shown. 2. The sum a + b is then the third side of the developed triangle as shown. By inspection it is seen that with these laws vector addition is commutative.