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Question
If `bar"a" = 2hat"i" + 3hat"j" - hat"k"`, `bar"b" = hat"i" - 4hat"j" + 2hat"k"`, find `(bar"a" + bar"b") xx (bar"a" - bar"b")`
Solution
Given: `bar"a" = 2hat"i" + 3hat"j" - hat"k"`,
`bar"b" = hat"i" - 4hat"j" + 2hat"k"`
∴ `bar"a" + bar"b" = (2hat"i" + 3hat"j" - hat"k") + (hat"i" - 4hat"j" + 2hat"k")`
`= 3hat"i" - hat"j" + hat"k"`
and `bar"a" - bar"b" = (2hat"i" + 3hat"j" - hat"k") - (hat"i" - 4hat"j" + 2hat"k")`
`= hat"i" + 7hat"j" - 3hat"k"`
∴ `(bar"a" + bar"b") xx (bar"a" - bar"b") = |(hat"i",hat"j", hat"k"),(3,-1,1),(1,7,-3)|`
`= (3 - 7)hat"i" - (- 9 - 1)hat"j" + (21 + 1)hat"k"`
`= - 4hat"i" + 10hat"j" + 22hat"k"`.
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