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Question
Find the magnitude of `vec"a" xx vec"b"` if `vec"a" = 2hat"i" + hat"j" + 3hat"k"` and `vec"b" = 3hat"i" + 5hat"j" - 2hat"k"`
Solution
The given vectors are `vec"a" = 2hat"i" + hat"j" + 3hat"k"`
`vec"b" = 3hat"i" + 5hat"j" - 2hat"k"`
`vec"a" xx vec"b" = |(hat"i", hat"j", hat"k"),(2, 1, 3),(3, 5, -2)|`
= `hat"i"(- 2 - 15) - hat"j"(- 4 - 9) + hat"k"(10 - 3)`
`vec"a" xx vec"b" = 17hat"i" + 13hat"j" + 7hat"k"`
`|vec"a" xx vec"b"| = |-17hat"i" + 13hat"j" + 7hat"k"|`
= `sqrt((-17)^2 + 13^2 + 7^2)`
`|vec"a" xx vec"b"| = sqrt(289 + 169 + 49)`
= `sqrt(507)`
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