Let $\mathbf{a}$ be a unit vector.  Compute
\[\|\mathbf{a} \times \mathbf{i}\|^2 + \|\mathbf{a} \times \mathbf{j}\|^2 + \|\mathbf{a} \times \mathbf{k}\|^2.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $\mathbf{a}$ be a unit vector.  Compute
\[\|\mathbf{a} \times \mathbf{i}\|^2 + \|\mathbf{a} \times \mathbf{j}\|^2 + \|\mathbf{a} \times \mathbf{k}\|^2.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
2
Let $\mathbf{a}$ be a unit vector.  Compute
\[\|\mathbf{a} \times \mathbf{i}\|^2 + \|\mathbf{a} \times \mathbf{j}\|^2 + \|\mathbf{a} \times \mathbf{k}\|^2.\]
train