Write any five properties of vector product of two vectors.

Explanation

(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 `vecA` and `vecB` may or may not be mutually orthogonal.
(ii) The vector product of two vectors is not commutative, i.e., `vecA xx vecB != vecB xx vecA` . But, `vecA xx vecB= -vecB xx vecA` .
Here it is worthwhile to note that `|vecA xx vecB|=|vecB xx vecA| = AB sintheta` 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.
(iii) The vector product of two vectors will have maximum magnitude when `sintheta= 1` , i.e., ` theta=90^(@)` i.e., when the vectors `vecA` and `vecB` are orthogonal to each other.
`(vecA xx vecB)_(max) = ABhatn`
(iv) The vector product of two non-zero vectors will be minimum when `sintheta = 1`, i.e., `theta= 0^(@) "or" 180^(@)`
`(vecA xx vecB)_(min)=0`
i.e., the vector product of two non-zero vectors vanishes, if the vectors are either parallel or antiparallel.
(v) The selt-eross product, i.e., product of a vcctor with itsclf is the null vector
`vecA xx vecA =A A sin 0^(@) hatn= 0`
In physics the mull vector 0 is simply denoted as zero.
(vi) The self-vector products of unit vectors are thus zero.
`hati xx hati = hatj xx hatj = hatk xx hatk =0`