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प्रश्न
Find the area of the traingle with vertices (1, 1, 0), (1, 0, 1) and (0, 1, 1).
उत्तर
Let A = (1, 1, 0), B = (1, 0, 1), C = (0, 1, 1)
|AB| = `sqrt((1 - 1)^2 + (1 - 0)^2 + (0 - 1)^2) = sqrt(0 + 1 + 1) = sqrt2`
|BC| = `sqrt((1 - 0)^2 + (0 - 1)^2 + (1 - 1)^2) = sqrt(1 + 1 + 0) = sqrt2`
|CA| = `sqrt((0 - 1)^2 + (1 - 1)^2 + (1 - 0)^2) = sqrt(1 + 0 + 1) = sqrt2`
∴ |AB| = |BC| = |CA|
∴ Triangle is an equilateral triangle
∴ Its area = `sqrt3/4 ("side")^2`
`= sqrt3/4 (sqrt2)^2`
`= sqrt3/2` sq.units.
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