Given that `vec(A) xx vec(B) = 0 , vec(B) xx vec(C ) = 0 , ` find the value of `vec(A) xx vec(C ) " if " vec (A) != 0 , vec(B ) != 0 , vec(B) != 0 and vec(C ) != 0 `

Explanation

To solve the problem step by step, we will analyze the given conditions and apply vector properties.

### Step 1: Understand the Cross Product
The cross product of two vectors \(\vec{A}\) and \(\vec{B}\) is given by:
\[ \vec{A} \times \vec{B} = |\vec{A}| |\vec{B}| \sin(\theta) \hat{n} \]
where \(\theta\) is the angle between the two vectors, and \(\hat{n}\) is the unit vector perpendicular to the plane containing \(\vec{A}\) and \(\vec{B}\).
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