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Given that vec(a). vec(b) =vec(a). vec(c...

Given that `vec(a). vec(b) =vec(a). vec(c )` Does this mean that `vec(b) = vec(c )` ?

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To determine whether \(\vec{b} = \vec{c}\) given that \(\vec{a} \cdot \vec{b} = \vec{a} \cdot \vec{c}\), we can analyze the situation step by step. ### Step 1: Understand the Dot Product The dot product of two vectors \(\vec{u}\) and \(\vec{v}\) is defined as: \[ \vec{u} \cdot \vec{v} = |\vec{u}| |\vec{v}| \cos(\theta) \] where \(\theta\) is the angle between the two vectors. ...
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