Find the area of the triangle with vertices at A(1, 0, 0), B(0, 2, 0), and C(0, 0, 3).
Answer and explanation
Correct answer: D. 7/2
- Step 1: Form vectors AB = (-1, 2, 0) and AC = (-1, 0, 3).
- Step 2: Compute cross product AB x AC: i(6 - 0) - j(-3 - 0) + k*(0 - (-2)) = (6, 3, 2).
- Step 3: Magnitude of cross product: |AB x AC| = sqrt(6^2 + 3^2 + 2^2) = sqrt(36 + 9 + 4) = sqrt(49) = 7.
- Step 4: Area of triangle = (1/2) * |AB x AC| = 7/2.
Answer
7/2.
Why not the others: 3 computes (1/2)6; 6 computes (1/2)12; 7 is the area of the parallelogram formed by the two vectors without the half factor.
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