Does the problem really say "product" of its speed and direction? I would interpret that as the scalar product of the length of your velocity vector with a unit vector in the direction of motion.

The "length" of is , the particle's speed. Divide each component of the velocity vector by that to get the unit vector in that direction.

Of course, the velocity vector is just the scalar product of that speed and unit vector since you would just be multiplying back in the speed you divided each component by.