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VECTOR PRODUCT OR CROSS PRODUCT, , > The vector or cross product of two vectors is defined as the vector who, magnitude is equal to the product of the magnitudes of two vectors and $s, of the angle between them and whose direction is perpendicular to the p, of the two vectors and is given by right hand rule., , , , , > Mathematically, if 6 is the angle between vectors A and B, then, AxB = |A| |B| Sin 0 A, where 7 is a unit vector perpendicular to the plane of A and B, and its, , direction is given by Right hand rule., , Thus direction of AxB is same as that of unit vector A.

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RIGHT HAND THUMB RULE, , Curl the fingers of the right hand in such a way that they, , point in the direction of rotation from vector A to vector B, through the smaller angle, then the stretched thumb points, in the direction of AxB.

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PROPERTIES OF VECTOR PRODUCT, , 1. The Vector Product is anti-commutative., AxB=—-BxA, , 2. The Vector Product is distributive over addition., Ax(B+C)=AxBt+Ax€, , 3. Vector Product of two parallel or anti-parallel vectors is a null vector., AxB = |A| |B| Sin (0° or 180°) A=0, , 4. Vector Product of a vector with itself is a null vector., , AxA = |A| |A| Sin 0° A =0, , , , , 5. The magnitude of the vector product of two mutually perpendicular vectors is equal to, the product of their magnitudes., , |AxB| = |A| |B] Sin 90° A = [A] |B|, , 6. The magnitude of each of the vectors t,f and & is 1 and the angle between any two of, them is 90°., , ix j=(1) (1) sin90° A =f