The angular momentum of a particle about a point is given by $L = mvr\sin\theta$, where $r\sin\theta$ is the perpendicular distance from the reference point (origin $O$) to the line of motion. Since the particle moves along a straight line $AB$, the perpendicular distance from the origin to this line remains constant. Assuming the magnitude of velocity $v$ is constant, the magnitude of angular momentum $L = mvr_{\perp}$ will also remain constant throughout the motion . The direction of angular momentum is also constant (perpendicular to the $XY$ plane). Therefore, the angular momentum at point $A$ is equal to the angular momentum at point $B$, i.e., $L_A = L_B$.