Question

if A*B=B*A then the angle between A and B is

Answer 1

Answer:

angle between A and B is 90¤ degrees .that means product of A and B is equal to product of B and A.

Answer 2

Answer:

hey mate

Explanation:

here is your answer

solution:

by right hand rule we also have

-N = B × A

eg the cross product of anticommutative

you provide the condition A × B = B × A

this must mean

N = -N

the only vector which satsifies this condition is the zero vector

A × B = B × A = 0

now we have

A = 0

B = 0

the angle between them is such that

A × B = 0

A B is not equal to 0

we know that important property of N :

A . N = A . (A × B ) = 0

therefore N is orthonogal vector

this is reinforced if we calculate

A × A = 0

therefore if let

$b \: = \alpha a \:$

where alpha is a scaler

then

$a \times b = \alpha a \times a = \alpha 0 = 0$

if alpha>0 then B is colinear - and the angle between the two vectors is alpha= 0

if alpha < 0 then B is antiparell - and the angle between the two vectors is theta = 180 =π radian

therefore there are three option for your condition to be met

. either A or B are the zero vector in which case the angle is undefined

. theta = 0° = 0 radian

.theta = 180° = π radian

$thanku$