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Question
Find the area of a parallelogram whose adjacent sides are determined by the vectors `veca = hati - hatj + 3hatk` and `vecb = 2hati - 7hatj + hatk`.
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Solution
`veca = hati - hatj + 3hatk`
`vecb = 2hati - 7hatj + hatk`
Area of parallelogram = `|veca xx vecb|`
Now `(veca xx vecb) = |(hati, hatj, hatk),(1, -1, 3),(2, -7, 1)|`
`(veca xx vecb) = hati(-1 + 21) - hatj(1 - 6) + hatk(-7 + 2)`
`(veca xx vecb) = 20hati + 5hatj - 5hatk`
`|veca xx vecb| = sqrt(20^2 + 5^2 + (-5)^2`
= `sqrt(450)`
= `15sqrt(2)` sq. units.
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