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Cross Product In mathematics and vector calculus, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space (R3) and is denoted by the symbol ×. Given two linearly independent vectors a and b, the cross product, a × b, is a vector that is perpendicular to both and therefore normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming. It should not be confused with dot product (projection product). If two vectors have the same direction (or have the exact opposite direction from one another, i.e. are not linearly independent) or if either one has zero length, then their cross product is zero. More generally, the magnitude of the product equals the area of a parallelogram with the vectors for sides; in particular, the magnitude of the product of two perpendicular vectors is the product of thei...

Scalars adding two or more scalars quantities is a simple thing and can be done by simple law of addition . like in this  example. A man walks 3km east and 4km north thus his total distance is 3km + 4km= 7km as distance is a scalar quantity so simple law of addition can be used . Vectors 1. Addition of vectors Two or more vectors may be added together to produce their  ADDITION . If two vectors have the same direction, their resultant has a magnitude equal to the sum of their magnitudes and will also have the same direction. Similarly orientated vectors can be subtracted the same manner. It follows that vectors can also be multiplied by a scalar, so for example if the vector  A  were multiplied by the number  m , the magnitude of the vector,  |A| , would increase to  m|A| , but its direction would not change. In general, since vectors may have any direction, we must use one of three methods for adding ...