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Let P be a plane passing through the poi...

Let P be a plane passing through the points (1,0,1),(1,-2,1) and (0,1,-2). Let a vector `vec(a) = alpha hat(i) + beta hat(j) + gamma hat(k)` be such that `vec(a)` is parallel to the plane P. perpendicular to `(hat(i) + 2hat(j) + 3hat(k)) and vec(a). (hat(i) + hat(j) + 2hat(k))`. then `(alpha - beta + gamma)^(2)` equals __________ .

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