Question:
If the angles between the sides of triangle ABC formed by A(2,3,5), B(-1,2,3), and C(3,5,-2) are \(\alpha, \beta, \gamma\), then \(\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma =\)
If the angles between the sides of triangle ABC formed by A(2,3,5), B(-1,2,3), and C(3,5,-2) are \(\alpha, \beta, \gamma\), then \(\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma =\)
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Use geometry properties or vector-based trigonometric identities to compute angle sums.
Updated On: Jun 4, 2025
- 1
- 2
- \(\dfrac{3}{2}\)
- \(\dfrac{1}{2}\)
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The Correct Option is B
Solution and Explanation
Use cosine rule and compute angles using vector dot products, then apply identity for sum of squares of sines of angles in triangle in 3D.
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