Calculate the area of a parallelogram whose diagonals are 3î + ĵ − 2k̂ and î − 3ĵ + 4k̂. A. 5√3 B. 10√3 C. 15 D. 20 Answer: A) 5√3 Explanation: Area = ½|d₁ × d₂|. d₁ × d₂ = î(4−6) − ĵ(12−(−2)) + k̂(−9−1) = −2î − 14ĵ − 10k̂. Magnitude = √(4 + 196 + 100) = √300 = 10√3. Area = ½(10√3) = 5√3.

imo class 12 vector algebra

Calculate the area of a parallelogram whose diagonals are 3î + ĵ − 2k̂ and î − 3ĵ + 4k̂.

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Calculate the area of a parallelogram whose diagonals are 3î + ĵ − 2k̂ and î − 3ĵ + 4k̂.

A. 5√3
B. 10√3
C. 15
D. 20

Answer: A) 5√3

Explanation: Area = ½|d₁ × d₂|. d₁ × d₂ = î(4−6) − ĵ(12−(−2)) + k̂(−9−1) = −2î − 14ĵ − 10k̂. Magnitude = √(4 + 196 + 100) = √300 = 10√3. Area = ½(10√3) = 5√3.

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