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Question
If `vec"r" * vec"a" = 0, vec"r" * vec"b" = 0` and `vec"r" * vec"c" = 0` for some non-zero vector `vec"r"`, then the value of `vec"a" * (vec"b" xx vec"c")` is ______.
Solution
If `vec"r" * vec"a" = 0, vec"r" * vec"b" = 0` and `vec"r" * vec"c" = 0` for some non-zero vector `vec"r"`, then the value of `vec"a" * (vec"b" xx vec"c")` is 0.
Explanation:
If `vec"r"` is a non-zero vector, then `vec"a", vec"b"` and `vec"c"` can be in the same plane.
Since angles between `vec"a"`, and `vec"c"` are zero
i.e. θ = 0
∴ `vec"a" * (vec"b" xx vec"c")` = 0
Hence the required value is 0.
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