Question

设向量a,b,c满足a+b+c=0,(a-b)⊥c,a⊥b.若|a|=1,则|a|²+|b|²+|c|²的值是__________.

Answer 1

答案:4

解析:∵a+b+c=0,a·b=0,

∴c=-(a+b).

∵(a-b)⊥c,∴(a-b)·［-(a+b)］=0,

即|a|²-|b|²=0.∴|a|=|b|=1.

∴|c|²=(a+b)²=|a|²+2a·b+|b|²=1+0+1=2.

∴|a|²+|b|²+|c|²=4.