If $OA$ and $BC$ are two-dimensional vectors that have the same magnitude, but $A(3,4), B(6,4)$ and $C(9,8)$, then is $OA=BC=3i+4j$?

Question

Diagram in reference to the question above.

Answer 1

$$\vec{OA}=(3-0,4-0)=(3,4)=3i+4j.$$ $$\vec{BC}=(9-6,8-4)=(3,4)=3i+4j.$$

Answer 2

Vectors only have a magnitude and a direction—they don’t have a location! So as you probably realized, $$\overrightarrow{OA}=\overrightarrow{BC} = 3\hat{\imath}+4\hat{\jmath}$$