What is the area of the triangle whose vertices are \((0, 7, 10)\), \((-1, 6, 6)\) and \((-4, 9, 6)\)?
\(9\) square units
Taking the vertices as \(A(0,7,10)\), \(B(-1,6,6)\), \(C(-4,9,6)\), the vectors \(\vec{AB}=(-1,-1,-4)\) and \(\vec{AC}=(-4,2,-4)\) give \(\vec{AB}\times\vec{AC}=(12,12,-6)\), whose magnitude is \(\sqrt{144+144+36}=18\). The area of the triangle is half this magnitude, that is, \(9\) square units.
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