因为 向量a、b、c两两所成的角相等
所以
(1)当向量a、b、c两两所成的角等于 0 度时 ,向量a,b,c同向,又 | a | =1,| b | =1,| c | = 3
所以 a+b+c = 5a | a+b+c | = 5 | a | = 5
(2)当向量a、b、c两两所成的角等于120 度时
| a+b+c | = √ | a+b+c | ^2 = √a^2 + b^2 + c^2 +2ab + 2ac + 2bc
=√a^2 + b^2 + c^2 +2|a||b| cos120 + 2|a||c|cos120 + 2|b||c|cos120
=√1^2 + 1^2 + 3^2 +2x1x1 cos120 + 2x1x3cos120 + 2x1x3cos120
= √1+ 1 + 9 - 1 - 3 - 3
=√4 = 2