Question

Determine the area of the triangle formed by the vectors u=(1,2,0) and v=(0,1,2)=

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1. Calculate the cross product of the vectors: \mathbf{u} \times \mathbf{v} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 1 & 2 & 0 \\ 0 & 1 & 2 \end{vmatrix} = 4 \mathbf{i} - 2 \mathbf{j} + 1 \mathbf{k}

2. Determine the magnitude of the resulting vector: \| \mathbf{u} \times \mathbf{v} \| = \sqrt{4^2 + (-2)^2 + 1^2} = \sqrt{21}

3. Use the magnitude to find the area: \text{Area} = \frac{1}{2} \sqrt{21}

The final answer is \frac{1}{2} \sqrt{21}

2. Determine the magnitude of the resulting vector:

3. Use the magnitude to find the area:

The final answer is

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