Can the vector product of two vectors be negative?

Answer 1

no .....the scalar product of two vectors never be negative

Yes it can If A is a vector, and B = -A, then A.B = -A2 which is negative. Always negative when the angle is between the vectors is obtuse.

Answer 2

Sure! The vector (cross) product involves the sine of the angle between the

first and second vectors. If the angle going counterclockwise from the first

to the second one is more than 180°, then its sine is negative, and so is the

cross-product.

Of course, in that case there's always an angle that's less than 180° ... if you go

counterclockwise from the second vector to the first. You get the same product of

the magnitudes that way, and the same 'sine', but with the opposite 'sign'. That's

exactly correct: The cross-product of two vectors has two equal and opposite values,

depending on the order in which you do it.

For example think of the 3 unit vectors in the x, y and z directions, usually called i, j and k where k = i X j (sometimes all written in Bold). Then j X i = -k .