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Question
If `hat"a", hat"b", hat"c"` are three unit vectors such that `hat"b"` and `hat"c"` are non-parallel and `hat"a" xx (hat"b" xx hat"c") = 1/2 hat"b"`, find the angle between `hat"a"` and `hat"c"`
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Solution
hat"a", hat"b", hat"c"` are unit vectors
`|vec"a"| = |vec"b"| = |vec"c"|` = 1
`hat"a" xx (hat"b" xx hat"c") = 1/2 hat"b"`
`(vec"a" * vec"c")vec"b" - (vec"a"*vec"b")*vec"c" = 1/2 vec"b"`
Comapre on both sides
`vec"a"*vec"c" = 1/2`
`vec"a"*vec"b"` = 0
⇒ `vec"a" ⊥ vec"b"`
`|vec"a"||vec"c"| cos theta = 1/2`
`(1)(1) costheta = 1/2`
∴ θ = `pi/3`
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