question about inner product formula

Status
Not open for further replies.

ran_out

Newbie level 6
Joined
Nov 24, 2003
Messages
13
Helped
0
Reputation
0
Reaction score
1
Trophy points
1,281
Activity points
111
hi all,

i have a question regarding the relation:

(x_transpose)y= norm_x* norm_y * cos(α)

where x, y are vectors and α is the angle between them.

from law of cosines u get:

cos(α) = (norm_ x^2 + norm y ^2 - norm_(x-y)^2) / (2*norm_x*norm_y)

right?

but how do you get the relation:

norm_ x^2 + norm y ^2 - norm_(x-y)^2 = 2*(x_transpose)y

which is needed to get the final result

(x_transpose)y = norm_x* norm_y * cos(α)

Thanx for help
 

According to the definition of the inner product,
norm_(x-y)^2=(x-y,x-y)
=norm_x^2-xy-yx+norm_y^2
=norm_x^2 + norm_y^2 - 2*(x_transpose)y

Therefore,
norm_ x^2 + norm y ^2 - norm_(x-y)^2
=2*(x_transpose)y.
 

huge thanx for that
 

Status
Not open for further replies.

Similar threads

Cookies are required to use this site. You must accept them to continue using the site. Learn more…