COMMUTATIVE LAW FOR DOT PRODUCT



COMMUTATIVE LAW FOR DOT PRODUCT
COMMUTATIVE LAW
FOR
DOT PRODUCT

This law states that :
“The scalar product of two vectors  and  is equal to the magnitude
of vector  times the projection of  onto the direction of vector . “
Consider two vectors  and  ,the angle between them is q.

where  represents the projection of vector  onto the direction of vector .
Similarly,
Where  represents the projection of vector  onto the direction of vector .
Since
This shows that the dot product of two vectors does not chanfe with the change in the order of the vectors to be multiplied.
This fact is known as the commutative of dot product.