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Find the area of the parallelogram whose adjacent sides are aijka¯=2i^-2j^+k^ and bijkb¯=i^-3j^-3k^ - Mathematics and Statistics

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Sum

Find the area of the parallelogram whose adjacent sides are `bar"a" = 2hat"i" - 2hat"j" + hat"k"` and `bar"b" = hat"i" - 3hat"j" - 3hat"k"`

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Solution

Given: `bar"a" = 2hat"i" - 2hat"j" + hat"k"` and `bar"b" = hat"i" - 3hat"j" - 3hat"k"`

∴ `bar"a" xx bar"b" = |(hat"i",hat"j",hat"k"),(2,-2,1),(1,-3,-3)|`

`= (6 + 3)hat"i" - (- 6 - 1)hat"j" + (- 6 + 2)hat"k"`

`= 9hat"i" + 7hat"j" - 4hat"k"`

`|bar"a" xx bar"b"| = sqrt(9^2 + 7^2 + (- 4)^2) = sqrt(81 + 49 + 16) = sqrt16`

Area of the parallelogram whose adjacent sides are `bar"a"` and `bar"b" = sqrt146` sq units.

Concept: Vector Product of Vectors (Cross)
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