# Transformation to Align Vectors

I have two vectors defined by $v_1=(x_1,y_1) - (x_2,y_2)$ and $v_2=(x_3,y_3)- (x_4,y_4)$. I want to find a transformation to align vector $v_2$ with vector $v_1$? Also is there a transformation which exists IF $v_1$ in not equal to $v_2$ in length? Vectors

• You need a transformation wich fix $v_1$ and rotates $v_2$ in the direction of $v_1$. $Tv_1=v_1$ and $Tv_2=kv_1,k\in\mathbb{R}$. – DiegoMath Jan 4 '18 at 15:05
• There is an infinite number of transformations that will “align” the vectors. You’ll need to explain what other properties you want the transformation to have, and what you’d like it to do to the rest of the plane. Are you looking for a rotation? A rigid motion that will also align the tails of the vectors? If they’re not the same length, do you want to stretch the first so that it matches the length of the second, too? If so, should this stretch be applied uniformly to everything else? Etc., etc., etc. – amd Jan 5 '18 at 1:51

Use this $v^{'}_{2}={{v_{1}.v_{2}\over |v_1|^2}v_1}$ in which "." indicates on inner product between two vectors.