Answer
See the figure below.
Work Step by Step
Assume that the terminal point of the vector $ a=\langle 1,3\rangle $, is $(x,y)$, then we have
$$\langle 1,3\rangle =(x,y) - (2,2)\Longrightarrow x=3, \quad y=5$$ and hence $ a $ is based at $(2,2) $ and the terminal point at $(3,5)$. So, the equivalent vector to $ a $ and based at the origin is $\langle 1,3\rangle $ as in the following figure.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/d630763a-310d-42b9-8217-c64353732f5c/steps_image/small_1568222769.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T001904Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=faa6a0956f1720b465efbe783245beae3eb61a5cd28f386f78044f98e9522d8a)