Q. Consider a vector $A$ that lies in $x y$-plane. If $A_{x}$ and $A_{y}$ are the magnitudes of its $x$ and $y$-components respectively, then the correct representation of $A$ can be given by
Motion in a Plane
Solution:
Vector along $X$-axis ( $x$-component)
$=A_{x} \hat{ i }=| A | \cos \theta \hat{ i }=A \cos \theta \hat{ i }$
Vector along $Y$ - axis ( $y$-component)
$=A_{y} \hat{ j }=| A | \sin \theta \hat{ j }=A \sin \theta \hat{ j }$
This can be shown as
