Three vectors extending from the origin are given as r₁ = (7, 3,−2), r₂ = (−2, 7,−3), and r₃ = (0, 2, 3). Find

(a) A unit vector perpendicular to both r₁ and r₂;

(b) A unit vector perpendicular to the vectors r₁ − r₂ and r₂ − r₃;

(c) The area of the triangle defined by r₁ and r₂;

(d) The area of the triangle defined by the heads of r₁, r₂, and r₃.