Word Count : 401

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To find the angle between two vectors \( \mathbf{A} \) and \( \mathbf{B} \), we can use the formula based on the dot product: \[ \cos \theta = \frac{\mathbf{A} \cdot \mathbf{B}}{|\mathbf{A}| |\mathbf{B}|} \] Where: - \( \mathbf{A} \cdot \mathbf{B} \) is the dot product of vectors \( \mathbf{A} \) and \( \mathbf{B} \), - \( |\mathbf{A}| \) and \( |\mathbf{B}| \) are the magnitudes of vectors \( \mathbf{A} \) and \( \mathbf{B} \), respectively. ### Step 1: Write the vectors We are given the vectors: \[ \mathbf{A} = 2\hat{i} - \hat{j} + \hat{k} \] \[ \mathbf{B} = 3\hat{i} + 4\hat{j} _____ __________ ______ _________ _______ ________ _______ _______ ________ ___ ____.
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