If $\vec{a}$ is any vector in space,then

• A
  $\vec{a} = (\vec{a} \cdot \hat{i})\hat{i} + (\vec{a} \cdot \hat{j})\hat{j} + (\vec{a} \cdot \hat{k})\hat{k}$
• B
  $\vec{a} = (\vec{a} \times \hat{i}) + (\vec{a} \times \hat{j}) + (\vec{a} \times \hat{k})$
• C
  $\vec{a} = \hat{j}(\vec{a} \cdot \hat{i}) + \hat{k}(\vec{a} \cdot \hat{j}) + \hat{i}(\vec{a} \cdot \hat{k})$
• D
  $\vec{a} = (\vec{a} \times \hat{i}) \times \hat{i} + (\vec{a} \times \hat{j}) \times \hat{j} + (\vec{a} \times \hat{k}) \times \hat{k}$