Question
Define unit vector and give its physical significance.

Answer

Unit vector: A vector having unit magnitude in a given direction is called a unit vector in that direction.
If $\vec{p}$ is a non zero vector $(P \neq 0)$ then the unit vector $\hat{ u }_{ p }$ in the direction of $\overrightarrow{ P }$ is given by,
$\hat{ u }_{ p }=\frac{\overrightarrow{ P }}{ P }$
$\therefore \overrightarrow{ P }=\hat{u}_p P$
Significance of unit vector:
$i.$ The unit vector gives the direction of a given vector.
$ii.$ Unit vector along $X, Y$ and $Z$ direction of a rectangular (three dimensional) coordinate is represented by $\hat{ i }, \hat{ j }$ and $\hat{ k }$ respectively Such that $\hat{ u }_x=\hat{ i }, \hat{ u }_y=\hat{ j }$ and $\hat{ u }_z=\hat{ k }$
This gives $\hat{i}=\frac{\vec{X}}{X}, \hat{j}=\frac{\vec{Y}}{X}$ and $\hat{k}=\frac{\vec{Z}}{Z}$

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