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Question
If `vec"a", vec"b", vec"c", vec"d"` are coplanar vectors, show that `(vec"a" xx vec"b") xx (vec"c" xx vec"d") = vec0`
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Solution
`vec"a" xx vec"b"` is ⊥r to `vec"a"` and `vec"b"`
`vec"c" xx vec"d"` is ⊥r to `vec"c"` and `vec"d"`
Since `vec"a", vec"b", vec"c"` and `vec"d"` are coplanar.
`vec"a" xx vec"b", vec"c" xx vec"d"` are ⊥r to same plane
`vec"a" xx vec"b"` parallel to `vec"c" xx vec"d"`
⇒ `(vec"a" xx vec"b") xx (vec"c" xx vec"d") = vec0`
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