(Solved): If V is any vector and n is any unit vector: b) Write the expression in index notation If \( \math ...

If V is any vector and n is any unit vector:

b) Write the expression in index notation

If \( \mathbf{v} \) is any vector and \( \hat{\mathbf{n}} \) is any unit vector: (a) Show that \( \mathbf{v} \) can be expressed as \( \mathbf{v}=(\mathbf{v} \cdot \hat{\mathbf{n}}) \hat{\mathbf{n}}+\hat{\mathbf{n}} \times(\mathbf{v} \times \hat{\mathbf{n}}) \) where the two terms represent components that are parallel and perpendicular to \( \hat{\mathbf{n}} \), respectively. (b) Write the equation given above in (a) in index notation.