Retrieving the out-of-plane blood flow velocity vector from two-dimensional transverse acquisitions of large vessels could improve the quantification of flow rate and maximum speed. The in-plane vector flow component can be computed easily using the Doppler frequency shift. The main problem is estimating the angle between the probe imaging plane and the vessel axis to derive the out-of-plane component from in-plane measurements. In this article, we study the case in which the velocity vector can be decomposed on two directions: the out-of-plane direction and the in-plane depth direction. We explore the combination of a technique called intrinsic spectral broadening with ultrafast plane wave imaging to retrieve the out-of-plane component of the flow velocity vector. Using a one-time probe calibration of this intrinsic spectral broadening, out-of-plane angle and flow speed can be recovered easily, thus avoiding approximations of a complex theoretical analysis. For the calibration step, ultrafast plane wave imaging permits a fast calibration procedure for the Doppler intrinsic spectral broadening. In vitro experimental validations are performed on a homogeneous flow phantom and a Poiseuille flow; the absolute speed was retrieved with 6% error. The potential of the technique is demonstrated in vivo on the human carotid artery. Combined with in-plane vector flow approaches, this out-of-plane Doppler imaging method paves the way to threedimensional vector flow imaging using only conventional onedimensional probe technology.