If OACB is a parallelogram with `vecOC=veca` and `vecAB=vecb`, then `vecOA` is equal to

Options

A. `veca+vecb`
B. `veca-vecb`
C. `(1)/(2)(vecb-veca)`
D. `(1)/(2)(veca-vecb)`

Answer

To find the vector \(\vec{OA}\) in the parallelogram \(OACB\) where \(\vec{OC} = \vec{a}\) and \(\vec{AB} = \vec{b}\), we can follow these steps:

### Step 1: Understand the properties of the parallelogram
In a parallelogram, opposite sides are equal and the diagonals bisect each other. We can use these properties to express the vectors in terms of \(\vec{a}\) and \(\vec{b}\).

### Step 2: Set up the equations using vector addition
From the parallelogram, we know:
\[ \vec{OC} = \vec{OA} + \vec{AB} \]
Substituting the known vectors:
\[ \vec{a} = \vec{OA} + \vec{b} \]

### Step 3: Rearranging the equation
We can rearrange the equation to express \(\vec{OA}\):
\[ \vec{OA} = \vec{a} - \vec{b} \]

### Step 4: Final expression for \(\vec{OA}\)
Thus, we have:
\[ \vec{OA} = \vec{a} - \vec{b} \]

### Step 5: Conclusion
The vector \(\vec{OA}\) is equal to \(\vec{a} - \vec{b}\).

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