If `vecX. vecY=vecX.vecZ, is vecY=vecZ` always?

Explanation

To determine whether \(\vec{Y} = \vec{Z}\) always holds true given that \(\vec{X} \cdot \vec{Y} = \vec{X} \cdot \vec{Z}\), we can follow these steps:

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