Vector product or cross product: The vector product of two vectors and is defined as the product of the magnitudes of and and the sine of the angle between them. If and creates angle θ then = AB. Where is the unit vector perpendicular to the plane of and . Properties of cross product:  = […]
Scalar product or dot product: The scalar product of two vectors and  is defined as the product of the magnitudes of and  and the cosine of the angle between them. If A and B creates angle θ then, . = AB . Properties of dot product: (i) . = BA  = AB  = . (ii)
Representation of a vector by coordinates: Let us consider OX, OY and OZ are three perpendicular axes, where O is the origin. Let P is a point with coordinates (x, y, z) and  =  is the position vector of P. , and are the unit vectors along + ve X, Y and Z axis. Let
Resolution of a vector into its components is the process to determining a set of vectors, whose resultant is the given vector. Each vector in that set is called a component of the given vector. Prove: Let us consider (= ) is resolute along the line OA and OB creates angles  and  with OC respectively.
Triangle law of vector addition: Statement: If two vectors are represented both in magnitude and direction by two sides of a triangle taken in the same order, then the resultant of these vectors is represented both in magnitude and direction by the third side of the triangle taken in the opposite order. Prove: Let us
Scalar: The quantities which are represented by magnitude and no directions and follow the ordinary algebra are called scalar quantity. Example: mass, volume, speed, density etc. Vector: The quantities which are represented by magnitude and directions and follow a special type of algebra (vector algebra) are called vector quantity. Example: velocity, acceleration, force etc. Representation
