physics_Vector

Let us assume that the vectors A, B, C are mutually perpendicular to each other
(Or) Vectors A, B&C be along x, y & z axis respectively (3 dimension).

BXC=B*C*Sin90=B*C*1=BC (because angle between vector B & C is 90)

Let us consider the resultant BC = P , where P is another vector
This vector P is along x-axis because according to cross product
Resultant is perpendicular to the plane containing given
Vectors (here given vector are B & C)

As vector A is perpendicular to B and C (mutually perpendicular)
Vector A & P are parallel or angle between them is 0(zero)

Thus AXP=A*P*Sin 0=0.

Mathematically,
AX (BXC) = AXP (where BXC = P)
So, AXP=0 (where angle between A & P is zero)

AX(BXC)=(AXB)XC=(AXC)XB=0=AX(CXB)=(BXA)XC=(CXA)XB
(BXC)XA=CX(AXB)=BX(AXC)=0=(CXB)XA=CX(BXA)=BX(CXA)

Note that Sin 180 = Sin 0 =0

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