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To transform the scene from the world coordinate system (WCS) to the viewing coordinate system (VCS), we follow the standard procedure of constructing a viewing transformation matrix. Part (a): WCS → VCS Transformation Given: * Viewpoint ( V = (2, -1, 3) ) * View plane normal ( \mathbf{n} = (3, -2, 4) ) * View-up vector ( \mathbf{v} = (0, 1, 2) ) Step 1: Compute the orthonormal basis vectors for the viewing coordinate system. * n-axis (view direction): unit vector along the view plane normal [ \mathbf{n_{unit}} = \frac{\mathbf{n}}{|\mathbf{n}|}, \quad |\mathbf{n}| = \sqrt{3^2 + (-2)^2 + 4^2} = \sqrt{9+4+16} = \sqrt{29} ] [ \mathbf{n_{unit}} = ____ ________ ______ _____ ___ ___ _________ _________ _________ ____ _____ _______.
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