Mention the properties of dot product of two vectors.

Explanation

(i)The vector product of any two vectors is always another whos direction is perpenduler to the plane containing these two vectors, orthogonal to both the vectors `vecA and vecB,` even through the vectors `vecA and vecB` may or may not be mutually orthogonal.
(ii) The vectors product of two vectors is not commutative, `vecA xx vecB ne vecB xx vecA`. But `vecA xx vecB=-vacB xx vecA`.
Here it is worthwhile to note that `|vecAxx vecB| ne |vecB| = |vecA|`. =AB `sin theta` in the case of the product vectors `vecA xx vecB and vecBxx vecA` , the magnitudes are equal but directions are opposite to eash other.
(iii) The vector product of two vectors will have maximum magnitude when `sintheta=1`, `theta=90^(@)`, when the vectors `vecA and vecB` are orthognal to each other.
`(vecA xx vecB)_(max) =ABhatn`.
(iv) The vector product of two non-zero vectors will be minimum when `sintheta=0`, or `theta=0^(@) or 180^(@)`
`(vecAB xx vecB)_(mi n)=0` .
the vector product of two non-zero vectors vanishes, if the vectors are either parallel or antiparallel.
(v) The self-cross product , product of a vector with itself is the null vector `vecA xx vecA= Asin 0^(@) hatn=vec0`
In phisics the null vector `vec0` is simply donated as zero,
The self-vectpr products of unit vectors are thus zero.
`hati xx hati=hatj xx hatj=hatk xx hatk=0` .