# Displacement Vector

## Displacement Vector

Displacement vector is a vector joining the initial position of the particle to its final position after an interval of time. Mathematically, it is equal to the change in position vector.

$$\Delta \overrightarrow{r}=\overrightarrow{{{r}_{B}}}-\overrightarrow{{{r}_{A}}}$$. Where,

$$\Delta \overrightarrow{r}$$ = Displacement Vector from point A to B.

The displacement of the particle would be the vector line AB, headed in the direction A to B. The direction of displacement vector is always headed from initial point to the final point.

The change in the position vector of an object is known as displacement vector. Suppose an object is at point A at time t = 0 and at point B at time t = t. The position vectors of the object at point A and at point B are:

Position vector at point A:

$$\overrightarrow{{{r}_{A}}}\,\,=\,\,5\widehat{i}+3\widehat{j}+4\widehat{k}$$.

Position vector at point B:

$$\overrightarrow{{{r}_{B}}}\,\,=\,\,2\widehat{i}+2\widehat{j}+1\widehat{k}$$.

Therefore, the displacement vector of the object from time interval 0 to t will be:

$$\Delta r\,\,=\,\,\overrightarrow{{{r}_{B}}}\,\,-\,\,\overrightarrow{{{r}_{A}}}\,\,=\,\,\left( 5\widehat{i}+3\widehat{j}+4\widehat{k} \right)\,\,-\,\,\left( \,2\widehat{i}+2\widehat{j}+1\widehat{k} \right)\,\,=\,\,3\widehat{i}+\widehat{j}+3\widehat{k}$$.

$$\Delta r\,\,=\,\,\overrightarrow{{{r}_{B}}}\,\,-\,\,\overrightarrow{{{r}_{A}}}\,\,=\,\,3\widehat{i}+\widehat{j}+3\widehat{k}$$.