Dot product:
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- The area is the area of the circular segment. The central angle \( heta\) subtended by the chord can be found using the dot product of vectors from the origin to the points.
- Let \( ec{OA} = \langle -1 + \sqrt{7}, 1 + \sqrt{7}
- angle\), \( ec{OB} = \langle -1 - \sqrt{7}, 1 - \sqrt{7}
- ec{OA} \cdot ec{OB} = (-1 + \sqrt{7})(-1 - \sqrt{7}) + (1 + \sqrt{7})(1 - \sqrt{7})
- = [(-1)^2 - (\sqrt{7})^2] + [1 - (\sqrt{7})^2] = (1 - 7) + (1 - 7) = -6 -6 = -12
- Magnitudes:
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