In space R^3, we define a scalar product by regulation
_(x1, y1, z1), (x2, y2, z2)_ = 2x1x2 + y1y2 + 2z1z2 + x1z2 +
(a)  Calculate the perpendicular projection of the point T (1,
1, 1) on the plane U in R3 with the equation x + 2y + 2z = 0 with
respect to the given scalar product.
(b)  Let _: R^3 _ R be a linear functional with _ (x, y, z) = x
+ 2y + 2z. Find the vector belonging to the functional _ according
to Riesz’s theorem with respect to a given scalar product.
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