Discuss the properties of scalar and vector

Explanation

Properties of vector (cross) product.
(i) The vector product of any two vectors is always another vector whose direction is perpendicular to the plane containing these two vectors, i.e., orthogonal to both the vectors `vecA` and `vecB` , even though the vectors`vec A` and `vecB` may or may not be mutually orthogonal.
(ii) The vector product of two vectors is not commutative, i.e., `vecA xx vecB ne vecB xx vecA` But , `vecA xx vecB = - [vec B xx vecA]`
Here it is worthwhile to note that `|vecA xx vecB| = |vecB xx vecA| = AB sin theta` i.e., in the case of the product vectors `vecA xx vecB` and `vecB xx vecA ` , the magnitudes are equal but directions are opposite to each other,
Properties of scalar product
(i) The product quantity `vecA . vecB` is always a scalar. It is positive if · the angle between the · vectors is acute (i.e.,< `90^@` ) and negative if the angle between them is obtuse
`(i.e. 90^@ lt theta lt 180^@ )` .
(ii) The scalar product is commutative, i.e ` vecA.vecB = vecB.vecA`
(iii) The vectors obey distributive law i.e `vecA (vecB + vecC) = vecA. vecB + vecA. vecC`
(iv) The angle between the vectors` theta = cos^(-1) [ (vecA.vecB)/(AB) ]`