Ex 10.4, 9 - Find area of triangle A(1, 1, 2), B(2, 3, 5) - Ex 10.4

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Ex 10.4, 9 Find the area of the triangle with vertices A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5). A (1, 1, 2) , B (2, 3, 5) , C (1, 5, 5) Area of triangle ABC is 1﷮2﷯ 𝐴𝐵﷯× 𝐴𝐶﷯﷯ 𝑨𝑩﷯ × 𝑨𝑪﷯ = 𝑖﷯﷮ 𝑗﷯﷮ 𝑘﷯﷮1﷮2﷮3﷮0﷮4﷮3﷯﷯ = 𝑖﷯ 2×3−4×3 ﷯− 𝑗﷯ 1×3−0×3 ﷯+ 𝑘﷯ 1×4−0×2 ﷯ = 𝑖﷯ 6−12﷯− 𝑗﷯(3−0) + 𝑘﷯ (4−0) = −6 𝒊﷯ – 3 𝒋﷯ + 4 𝒌﷯ Magnitude of 𝐴𝐵﷯ × 𝐴𝐶﷯ = ﷮ −6﷯2+ −3﷯2+42﷯ 𝐴𝐵﷯ × 𝐴𝐶﷯﷯ = ﷮36+9+16﷯ = ﷮61﷯ Area of triangle ABC = 1﷮2﷯ 𝐴𝐵﷯ × 𝐴𝐶﷯﷯ = 1﷮2﷯ × ﷮61﷯ = ﷮61﷯﷮2﷯ Therefore, the required area is ﷮𝟔𝟏﷯﷮𝟐﷯ .

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