Question

The area of the triangle with vertices \( (1, 2, 0), (1, 0, 2) \), and \( (0, 3, 1) \) in square units is

• A. \( \sqrt{5} \)
• B. \( \sqrt{7} \)
• C. \( \sqrt{6} \)
• D. \( \sqrt{3} \)

Hint:

To find the area of a triangle in 3D, use the formula involving the cross product of two vectors.

Answer 1

The Correct Option is C

Step 1: Using the formula for the area of a triangle.
The area of a triangle with vertices \( (x_1, y_1, z_1), (x_2, y_2, z_2), (x_3, y_3, z_3) \) is given by: \[ \text{Area} = \frac{1}{2} \left| \vec{A} \times \vec{B} \right| \] where \( \vec{A} \) and \( \vec{B} \) are vectors formed by the coordinates of the vertices. Step 2: Computing the cross product.
After calculating the vectors and their cross product, the area is found to be \( \sqrt{6} \). Step 3: Conclusion.
Thus, the correct answer is (C).