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To find the direction cosines of the perpendicular from the origin to the given plane, we need to follow these steps: ### Step 1: Identify the normal vector to the plane The equation of the plane is: \[ \mathbf{r} \cdot (6\mathbf{i} + 4\mathbf{j} + 2\sqrt{3}\mathbf{k}) + 2 = 0 \] The vector normal to the plane is given by the coefficients of the unit vectors \( \mathbf{i}, \mathbf{j}, \mathbf{k} \). So, the normal vector \( \mathbf{n} \) to the plane _____ _______ _______ ___ __________ ____ ___.
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