Word Count : 487

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### Part 1: Obtain a Unit Vector Perpendicular to the Plane of Vectors \( \vec{A} \) and \( \vec{B} \) We are given the following vectors: \[ \vec{A} = 3\hat{i} - 4\hat{j} + 2\hat{k} \] \[ \vec{B} = \hat{i} + 3\hat{k} \] To find a unit vector perpendicular to the plane of these vectors, we need to compute the cross product \( \vec{A} \times \vec{B} \). The cross product of two vectors gives a vector that is perpendicular to both. Let's compute the cross product \( \vec{A} \times \vec{B} \): \[ \vec{A} = (3, -4, 2), \quad _________ __________ ____ ___ _______ _______ ____ __________ _____.
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