the cosine between two vectors represented by the XYZ component vectors.

24 Views Asked by At

the original text is:

Let $n$ be any direction in the space, The projection of vector $A$ on the $n$ direction is : $A_n = |A| cos (n,A)$.\ or, notice the equation we have already know in the analytical geometry that the cosine of the angle between two vectors is :\ $A_n =| A| [cos(n,X)cos(A,X)+ cos(n,Y)cos(A,Y)+cos(n,Z)cos(A,Z)] = A_x cos(n,X) +A_ycos(n,Y)+A_z cos(n,Z)$

OK,I know I am very stupid, but I just can't understand how he get
$cos(n,A)=cos(n,X)cos(A,X)+ cos(n,Y)cos(A,Y)+cos(n,Z)cos(A,Z)$
I have tried to search this on wikipedia related to the vector topic, but gain nothing basically.
Thank you!

1

There are 1 best solutions below

0
On BEST ANSWER

Your term is an awkward way of writing out $n_x \cdot A_x + n_y \cdot A_y + n_z \cdot A_z$, that is, a simple dot product ${\bf n} \cdot {\bf A}$.