If `vec A. vec B = vec A. vec C`, is it correct to conclude that ` vec B =vec C` ?

Explanation

To determine whether the equation \( \vec{A} \cdot \vec{B} = \vec{A} \cdot \vec{C} \) implies that \( \vec{B} = \vec{C} \), we can analyze the situation step by step.

### Step 1: Understand the Dot Product
The dot product of two vectors \( \vec{A} \) and \( \vec{B} \) is given by the formula:
\[ \vec{A} \cdot \vec{B} = |\vec{A}| |\vec{B}| \cos \theta_1 \]
where \( \theta_1 \) is the angle between vectors \( \vec{A} \) and \( \vec{B} \).
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