Question

For any vectors \({\rm{u}}\)and\({\rm{v}}\)in\({{\rm{V}}_{\rm{3}}}{\rm{,u \times v = v \times u}}\).

Short answer

The answer for the given statement is False.

Step-by-step solution

Right-Hand rule.

The right-hand rule for the direction of\({\rm{a \times b}}\)

To expose that the assertion is false as it contradicts the right-hand rule this is used to provide the direction of the cross product of two vectors.

Direction of Vectors.

(1) Ensure that the two vectors are placed in a manner that their tails are touching, in this situation, they already are touching.

(2) Make your fingers straight and hold your proper palm such that your arms are initially pointing inside the direction of the vector\({\rm{a}}\).

(3) Curl your fingers from vector\({\rm{a}}\)in the direction of\({\rm{b}}\), once you are performing curling, make sure that your thumb is pointing perpendicular to your palms as if you are giving a thumbs up.

The direction of your thumb is now the direction of the vector\({\rm{a \times b}}\).

Therefore, the given statement contradicts the fact, the answer is false.