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Sometimes, we will get situations where we need to calculate the angle between 2 forces, or 2 sides on an object in 3D space. In that case, using the dot product can be really helpful. So if we have 2 vectors with an angle, we can write the dot product like this. If youre trying to find the angle, we can write the equation like this to calculate the angle between the 2 sides. In another situation, we might need to find the components of a vector that is parallel and perpendicular to a line. The parallel component is sometimes shown like this, or like this, and its referred to as the projection of a force. To find it, all we do is take the dot product between the force expressed in cartesian form and the unit vector of the axis, or side where the projection is supposed to be. If we need to find the perpendicular component, then we can use this equation to do it, which is just the Pythagorean theorem. Here, A is the magnitude of the force, this is the para
