设向量 $\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}$ 满足 $\boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}=0,(\boldsymbol{a}-\boldsymbol{b}) \perp \boldsymbol{c}, \boldsymbol{a} \perp \boldsymbol{b}$, 若 $|\boldsymbol{a}|=1$, 则 $|\boldsymbol{a}|^{2}+|\boldsymbol{b}|^{2}+|\boldsymbol{c}|^{2}$ 的值是
$\because a+b+c=0, \quad \therefore c=-(a+b) . \because(a-b) \perp c, \quad \therefore(a-b) \cdot[-(a+b)]=0$. 即 $|a|^{2}-|b|^{2}=0, \quad \therefore|a|=|b|=1$,

$\because a \perp b, \quad \therefore a \cdot b=0, \quad \therefore|c|^{2}=(a+b)^{2}=|a|^{2}+2 a \cdot b+b^{2}=1+0+1=2$.

$\therefore|a|^{2}+|b|^{2}+|c|^{2}=4$.