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Ex 10.4, 10 - Find area of parallelogram whose adjacent sides - Ex 10.4

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  1. Class 12
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Ex 10.4, 10 Find the area of the parallelogram whose adjacent sides are determined by the vectors 𝑎﷯ = 𝑖﷯ − 𝑗﷯ + 3 𝑘﷯ and b = 2 𝑖﷯ − 7 𝑗﷯ + 𝑘﷯ . 𝑎﷯ = 𝑖﷯ − 𝑗﷯ + 3 𝑘﷯ = 1 𝑖﷯ − 1 𝑗﷯ + 3 k﷯ 𝑏﷯ = 2 𝑖﷯ − 7 𝑗﷯ + 𝑘﷯ = 2 𝑖﷯ − 7 𝑗﷯ + 1 k﷯ Area of parallelogram ABCD = 𝑎﷯ × 𝑏﷯﷯ 𝒂﷯ × 𝒃﷯ = 𝑖﷯﷮ 𝑗﷯﷮ 𝑘﷯﷮1﷮−1﷮3﷮2﷮−7﷮1﷯﷯ = 𝑖﷯ (−1 × 1 − (−7) × 3) − 𝑗﷯ (1 × 1 − 2 × 3) + 𝑘﷯ (1 × −7 − 2 × −1) = 𝑖﷯ (−1−(−21)) − 𝑗﷯ (1 − 6) + 𝑘﷯ (−7 −(−2)) = 𝑖﷯ (−1 + 21) − 𝑗﷯ (−5) + 𝑘﷯ (−7 + 2) = 20 𝒊﷯ + 5 𝒋﷯ − 5 𝒌﷯ Magnitude of 𝑎﷯ × 𝑏﷯ = ﷮202+52+ −5﷯2﷯ 𝑎﷯ × 𝑏﷯﷯ = ﷮400+25+25﷯ = ﷮450﷯ = ﷮25×9×2﷯ = 5 × 3 × ﷮2﷯ = 15 ﷮2﷯ Therefore, the area of parallelogram is 15 ﷮𝟐﷯ .

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