Question

Explain that the cross prduct of two vector does not obey commutative law

Answer 1

Question

Explain that the cross prduct of two vector does not obey commutative law

Answer

Firstly,

Commutative Law states that

$\large{ \sf{p \times q =q \times p }}$

Cross Product

$\displaystyle{ \large{ \sf{ \vec{a} \times \vec{b} = | \vec{a}| | \vec{b}| \sin( \alpha ) }}}$

Direction of vectors in cross product is given by Right Hand Thumb Rule

Assume the cross product of two vectors to direct towards east. The direction changes of the product changes when the vectors are reversed. Mathematically,

$\displaystyle{ \large{ \sf{ \vec{a} \times \vec{b} = - \: \vec{b} \times \vec{a} }}}$

Consider "b" to be on the postive x - axis,when it is reversed it directs towards the negative x - axis and bear negative magnitude. Hence,the result

Since, this violates the commutative rule.

Cross Product of Two Vectors doens't obey Commutative Law