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Question
If `vec"a" = hat"i" - 2hat"j" + 3hat"k", vec"b" = 2hat"i" + hat"j" - 2hat"k", vec"c" = 3hat"i" + 2hat"j" + hat"k"`, find `vec"a" xx (vec"b" xx vec"c")`
Solution
`vec"b" xx vec"c" = |(hat"i", hat"j", hat"k"),(2, 1, -2),(3, 2, 1)|`
= `hat"i"(1 + 4) - hat"j"(2 + 6) + hat"k"(4 - 3)`
= `5hat"i" - 8hat"j" + hat"k"`
`vec"a" xx vec"b" xx vec"c" = |(hat"i", hat"j", hat"k"),(1, -2, 3),(5, -8, 1)|`
= `hat"i"(- 2 + 24) - hat"j"(1 - 15) + hat"k"(- 8 + 10)`
= `22hat"i" + 14hat"j" + 2hat"k"`
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