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Question
If `vec"a" = hat"i" + 2hat"j" + 3hat"k", vec"b" = 2hat"i" - hat"j" + hat"k", vec"c" = 3hat"i" + 2hat"j" + hat"k"` and `vec"a" xx (vec"b" xx vec"c") = lvec"a" + "m"vec"b" + ""vec"c"`, find the values of l, m, n
Solution
Given `vec"a" xx (vec"b" xx vec"c") = lvec"a" + "m"vec"b" + "n"vec"c"`
`(vec"a"*vec"c")vec"b" - (vec"a"*vec"b")vec"c" = lvec"a" + "m"vec"b" + "n"vec"c"`
Compare ```vec"a", vec"b", vec"c"` on both sides
l = 0
m = `vec"a"*vec"c"`
n = `- (vec"a"*vec"b")`
m = 3 + 4 + 3, n = – (2 – 2 + 3)
m = 10, n = – 3
l = 0, m = 10, n = – 3
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