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Question
`vec"a" = 2hat"i" + 3hat"j" - hat"k", vec"b" = -hat"i" + 2hat"j" - 4hat"k", vec"c" = hat"i" + hat"j" + hat"k"` then find the va;ue of `(vec"a" xx vec"b")*(vec"a" xx vec"c")`
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Solution
`vec"a" xx vec"b" = |(hat"i", hat"j", hat"k"),(2, 3, -1),(-1, 2, -4)|`
= `hat"i"(- 12 + 2) - hat"j"(- 8 - 1) + hat"k"(4 + 3)`
= `-10hat"j" + 9hat"j" + 7hat"k"`
`vec"a" xx vec"c" = |(hat"i", vec"j", vec"k"),(2, 3, -1),(1, 1, 1)|`
= `hat"i"(3 + 1) - hat"j"(2 + 1) + hat"k"(2 - 3)`
= `4hat"i" - 3hat"j" - hat"k"`
`(vec"a" xx vec"b")*(vec"a" xx vec"c")` = (– 10)4 + 9(– 3) + 7(–1)
= – 40 - 27 – 7
= – 74
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