Oblique Projection

Geometry Level 4

Given a plane that passes through the point \( r_0 = (1, 2, -1) \), and has a normal vector of \( (2, 3, -2) \), we want to find the oblique (i.e. non-orthogonal) projection of the point \( p_0 = ( 33, 34, 47 ) \) on the specified plane along the oblique direction given by \( \mathbf{d} = ( -3, 6, -2) \). Let the projected point be \( ( a, b, c ) \), what is the value of \( a + b + c \) ?

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