Justin R. answered • 11/24/20

University professor and winner of multiple teaching awards

The number is 3 isn't important, what is important is that 3 is a scalar quantity. So we are seeking an expression involving vectors that reduces to a scalar.

- (u x v) • (v x w) = vector * vector = scalar
- u x (u - w) = vector x vector = vector
- (u • v) (u + w) = scalar * vector = vector
- ||u + v|| w = scalar * vector = vector

So only the first produces a scalar, so that's the answer.