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 ______.

Answer 1

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.