 Now with this more nuanced understanding about vectors and how to do equations with them You might look back at the previous things we've done and see equations like this the equation for the force due to gravity Is equal to the mass times acceleration due to gravity or you might see the simple model for the force due to friction Where the frictional force is just equal to some constant times the normal force Now you'll notice there are no arrows on these equations We could put the arrows back on here So you know the force is a vector and the acceleration must be a vector we say well We know that the force of gravity must be straight down the acceleration must be straight down So we could do that or we could say well We know what direction is and all we were talking about here is the magnitude So we know the magnitude of that force vector is equal to the mass times a known Magnitude of the acceleration due to gravity on earth now in the frictional force case We definitely can't put the arrows on here because those things are not in the same direction if we have a block on a Surface and it's got a normal force stopping the block from falling through that surface The frictional force is in a different direction. So this is definitely wrong Okay, so that is definitely not an equation that is a vector equation That is definitely an equation that is just talking about the magnitude of the frictional force compared to some constant times the Magnitude of the normal force. So that is definitely a scalar equation Another way of looking at this one back here is that it's the Z component It's the downward component of the gravitational force and The downward component of the acceleration due to gravity and the other two components happen to be zero And so there are two possible things you could mean when you have a equation using things that are vectors with no arrows on top And the first is it's just a representation of a single component of a vector equation And the second is that we're just talking about the magnitude of those vectors and which is the correct one Well, you have to get that from context. This is why it's very important to define your variables very carefully and the symbols That you use very carefully