Oct 12, 2005 #1 R 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
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
Oct 12, 2005 #2 S steve10 Full Member level 3 Joined Mar 26, 2002 Messages 175 Helped 32 Reputation 64 Reaction score 0 Trophy points 1,296 Location Los Angeles (Chinese) Activity points 2,538 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.
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.
Oct 12, 2005 #3 R 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 huge thanx for that