In the figure, the vectors $\vec a$ and $\vec b$ lie on the floor, and $\vec a\times\vec b$ points straight up. Which statement about $\vec b\times\vec a$ is correct?

Fig. 1: A three-dimensional picture with right-handed axes, z up, x towards the viewer on the left and y to the right. Two vectors lie on the floor and start at the origin: a blue arrow a along the x-axis and a green arrow b pointing to the right. The floor parallelogram on them is lightly shaded, and the angle theta between a and b is marked in orange. A thick red arrow labelled a cross b runs straight up from the origin, at right angles to both a and b.