If `vec(A) vec(B), vec(C )` are three vectors and one of them has zero magnitude , then given that `vec(A) xx vec(B) = 0 and vec(B) xx vec(C ) = 0 ` , Prove that `vec(A) xx vec(c ) = 0 `

Explanation

To prove that \(\vec{A} \times \vec{C} = 0\) given the conditions \(\vec{A} \times \vec{B} = 0\) and \(\vec{B} \times \vec{C} = 0\), we can follow these steps:

### 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 vectors, and \(\hat{n}\) is the unit vector perpendicular to the plane formed by \(\vec{A}\) and \(\vec{B}\).
...