[SOLVED] physical meaning of dot product and cross product

[eng_boody]

Please i'd like to know the physical meaning of dot product an how it was originated and why it return a scalar quantity as well as the physical meaning of the vector product and why the result vector is perpendicular to both the multiplicated vectors and how it was originated.....note that i don,t need the formula..i know it A.B=abcos(theta)....A X B=absin(theta)n.....i just want the physical meaning ....

 

[tallface65]

A dot product conceptually is the projection that one vector has over another. This is why it is a scalar, it only tells the length of the projection. Another way of thinking is that it tells one how 'parallel' the two vectors are to one another. The larger a dot product between two unit vectors, the smaller the angle is between them in a given plane or more obtuse if the angle is greater than 90 degrees (the more parallel they are).

A cross product results in a vector that has a direction that is perpendicular to both vectors and a magnitude that is equal to the parallelogram with side lengths equal to the magnitudes of the two vectors and a skew equal to the angle between the vectors. Another way of thinking is that it, conversely to the dot product, tells one how 'perpendicular' the two vectors are. The larger the magnitude of the cross product between two unit vectors, the larger the angle between the vectors (up to 90 degrees) in a given plane (the more perpendicular they are).

Have Fun

 

[eng_boody]

Thnx tallface65 ..

u said that dot product represents the scalar value of the projection of a vector over a another vector....my question here is if i have vector (A) and vector (B) of magnitudes (a)
and (b) respectively...and the angle between them is theta ....so the projection(i am not sure is it the component??) of vector A in direction of B is a*cos(theta)...not a*b*cos(theta)...why did we multiplied by b (generally b is not necessary to be 1) then .....is there a difference between the projection and the component of a vector (of course in some direction)......or what is the reason of multiplying by b .

thnx

 

[blooz]

Projection of B in the direction of A is

\[B\cos(\theta)\]

Projection of A in the direction of B is
\[A\cos(\theta)\]

how much these two vectors point in the same direction. ?

it's calculated as a product of these two
as \[AB\cos(\theta)\]

h**p://behindtheguesses.blogspot.com/2009/04/dot-and-cross-products.html

 

[eng_boody]

thank u so much ..