Show that : `[vecl vecm vecn] [veca vecb vecc]=|(vecl.veca, vecl.vecb, vecl.vecc),(vecm.veca, vecm.vecb, vecm.vecc),(vecn.veca, vecn.vecb, vecn.vecc)|`

Explanation

To show that \([ \vec{l} \vec{m} \vec{n} ] [ \vec{a} \vec{b} \vec{c} ] = |( \vec{l} \cdot \vec{a}, \vec{l} \cdot \vec{b}, \vec{l} \cdot \vec{c} ), ( \vec{m} \cdot \vec{a}, \vec{m} \cdot \vec{b}, \vec{m} \cdot \vec{c} ), ( \vec{n} \cdot \vec{a}, \vec{n} \cdot \vec{b}, \vec{n} \cdot \vec{c} )|\), we will follow these steps:

### Step 1: Define the vectors
Let:
- \(\vec{l} = l_1 \hat{i} + l_2 \hat{j} + l_3 \hat{k}\)
- \(\vec{m} = m_1 \hat{i} + m_2 \hat{j} + m_3 \hat{k}\)
- \(\vec{n} = n_1 \hat{i} + n_2 \hat{j} + n_3 \hat{k}\)
- \(\vec{a} = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k}\)
...