Question - Simplifying Vector Equations
Solution:
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$$\vec{AC}$$**
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