Problem 20 - Entrance Test
Find the area of the triangle with vertices A(1, 1, 1), B(1, 2, 3), and C(2, 3, 1).
Correct: A
Vector AB = B - A = (1-1, 2-1, 3-1) = (0, 1, 2). Vector AC = C - A = (2-1, 3-1, 1-1) = (1, 2, 0). Area of the triangle = (1/2) |AB x AC|. AB x AC = |i j k; 0 1 2; 1 2 0| = i(0 - 4) - j(0 - 2) + k(0 - 1) = -4i + 2j - k = (-4, 2, -1). |AB x AC| = √((-4)² + 2² + (-1)²) = √(16 + 4 + 1) = √21. Area of the triangle = (1/2)√21 = √21/2. Error, ABXAC should be 1/2 (6) = 3