Simplifying Vector Equations
The question is asking to simplify vector equations. Let's solve the first part a):
**a) \(\vec{AM} + \vec{AC} + \vec{MC}\)**
To simplify this, we use the concept that a vector going from point A to point C (\(\vec{AC}\)) is the same as going from A to M (\(\vec{AM}\)) added to going from M to C (\(\vec{MC}\)). Symbolically:
**\(\vec{AM} + \vec{MC} = \vec{AC}\)**
Using this property, we can replace \(\vec{AM} + \vec{MC}\) in the initial equation with \(\vec{AC}\). So the equation simplifies to:
**\(\vec{AC} + \vec{AC}\)**
When we add a vector to itself, we are just doubling the length of the vector in the same direction. Therefore, the final simplified expression is:
**2\(\vec{AC}\)**
