SOME ANALYTICAL TOOLS

VECTORS AND VECTOR ANALYSIS A DIRECTED LINE SEGMENT IS CALLED A VECTOR. THE LENGTH IS CALLED THE LENGTH OF THE VECTOR. AND THE DIRECTION IS CALLED THE DIRECTION OF THE VECTOR. TWO VECTORS ARE EQUAL IF AND ONLY IF THEY HAVE THE SAME LENGTH AND THE SAME DIRECTION. THE LENGTH OF A VECTOR IS CALLED THE EUCLIDEAN NORM OR MAGNITUDE. INNER PRODUCT(DOT PRODUCT) THIS IS ALSO CALLED SCALAR PRODUCT THE RESULT IS A SCALAR a.b = |a||b|cosϒ for a=/= 0, b=/= 0 a.b = 0 a=0 or b=0 and ϒ(0<ϒ<π) IS ANGLE B/W a&b THIS IS COMPUTED WHEN THE VECTORS HAVE THEIR INITIAL POINT COINCIDING. VECTOR PRODUCT ( CROSS PRODUCT) THE RESULT IS A VECTOR Axb (or a^b) v = axb = 0 THIS IS THE CASE IF AND ONLY IF THE VECTORS a AND b HAVE THE SAME OR OPPOSITE DIRECTION OR ONE OF THESE VECTORS IS THE ZERO VECTOR. IN ANY OTHER CASE, v = axb LENGTH = AREA OF PARALLELOGRAM WHOSE SIDES ARE a & b. DIRECTION = PERPENDICULAR TO BOTH a AND b a,b,v FORM A RIGHT HANDED TRIPLE OR RIGHT HANDED TRIAD |v|=|a||b|sinϒ