Find the area of a triangle with vertices A(1, 1, 2), B(2, 3, 5), and C(1, 5, 5). A. √61/2 B. √61 C. 61/2 D. √30 Answer: A) √61/2 Explanation: AB = î + 2ĵ + 3k̂. AC = 0î + 4ĵ + 3k̂. AB × AC = î(6−12) − ĵ(3−0) + k̂(4−0) = −6î − 3ĵ + 4k̂. Area = ½|AB × AC| = ½√(36 + 9 + 16) = ½√61 = √61/2.

imo class 12 vector algebra

Find the area of a triangle with vertices A(1, 1, 2), B(2, 3, 5), and C(1, 5, 5).

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Find the area of a triangle with vertices A(1, 1, 2), B(2, 3, 5), and C(1, 5, 5).

A. √61/2
B. √61
C. 61/2
D. √30

Answer: A) √61/2

Explanation: AB = î + 2ĵ + 3k̂. AC = 0î + 4ĵ + 3k̂. AB × AC = î(6−12) − ĵ(3−0) + k̂(4−0) = −6î − 3ĵ + 4k̂. Area = ½|AB × AC| = ½√(36 + 9 + 16) = ½√61 = √61/2.

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