A.B=C.B, but A ≠C

Suppose that A is perpendicular to B;

B is along the west direction.

Also, B is perpendicular to C;

A and C are along the south and north directions, respectively

A is perpendicular to B, so their dot or scalar product is zero. i.e.,

B is perpendicular to C, therefore, their dot or scalar product is zero. i.e.,

∴A �B=B �C, but A≠C Hence, proved.