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Question
Find the area of the parallelogram whose adjacent sides are determined by the vector `veca = hati - hatj + 3hatk` and `vecb = 2hati - 7hatj + hatk`.
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Solution
`veca = hati - hatj + 3hatk, vecb = 2hati - 7hatj + hatk`
Here, `veca xx vecb = |(hati, hatj, hatk), (2, 3, 4), (4, 6, 8)|`
= `hati(-1 + 21) - hatj(1 - 6) + hatk(-7 + 2)`
= `20hati + 5hatj - 5hatk`
∴ Area of parallelogram = `veca xx vecb`
= `|veca xx vecb| = sqrt((20)^2 + 5^2 + 5^2)`
`= sqrt450`
`= 15sqrt2` square unit.
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