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College physics, why should we multiply it by a unit vector et?
V is a vector, there must be a direction, and the front ds/dt is the size.

In advanced mathematics, numerical values are directional, such as+for forward and-for backward. The unit vector can actually be understood as signed 1.

It is necessary to decompose the poles to the direction perpendicular to the force to calculate the length. M=rF, R is the position vector from the fulcrum of the rotating shaft to the point of force application, and all three are vectors. The size is m = rfsin (the angle between r and f). Your angle here should be the angle between the pole and the ground, so it becomes cos.

meaning

In physics and engineering, geometric vectors are more often called vectors. Many physical quantities are vectors, such as the displacement of an object, the force exerted on it by a ball hitting a wall and so on. On the contrary, it is scalar, that is, a quantity with only size and no direction. Some definitions related to vectors are also closely related to physical concepts. For example, vector potential corresponds to potential energy in physics.

Baidu Encyclopedia-Unit Vector