When a translation by v rightarrow is composed with a transl

When a translation by v rightarrow is composed with a translation by w rightarrow, what type of transformation is the composition? Prove your answer. Be sure to: Specify the composition precisely in terms of v rightarrow and w rightarrow. Address whether it matters in which order the composition is performed.

Solution

First we translate say vector:x by v giving:x\'=x+v

Now we translate by w giving:x\'\'=x\'+w=x+v+w

Hence the composition is translation by:v+w ie the composition is another translation given by sum of two vectors

The order is not important here as addition of vectors is commutative