Word Count : 507

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To find a vector of magnitude 6 that is perpendicular to both given vectors, we can follow these steps: ### Step 1: Identify the vectors The two given vectors are: 1. \( \mathbf{A} = 2\hat{j} - \hat{j} + 2\hat{k} = \hat{j} + 2\hat{k} \) 2. \( \mathbf{B} = 4\hat{i} - \hat{j} + 3\hat{k} \) ### Step 2: Compute the cross product of the two vectors The cross product of two vectors \( \mathbf{A} = A_x \hat{i} + A_y \hat{j} + A_z \hat{k} \) and \( \mathbf{B} = B_x \hat{i} + B_y \hat{j} + B_z \hat{k} \) is given by the determinant: \[ \mathbf{A} \times \mathbf{B} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ A_x & A_y & A_z \\ B_x & B_y & B_z \end{vmatrix} \] __________ _______ ____ __________ ______ ____ __________ ________ ________.
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