Question

已知向量a、b满足|a|=3，|b|=2，|a+b|=4，则|a-b|=？

Answer 1

|a+b|=4
(a+b)^2=16
|a|^2+|b|^2+2a*b=16
9+4+2a*b=16
2a*b=3

|a-b|^2
=(a-b)^2
=|a|^2+|b|^2-2a*b
=9+4-3
=10

|a-b|=√10请点击“采纳为答案”

Answer 2

解：∵|a+b|=√(lal�0�5 +2a*b+lbl�0�5 ) =4
∴2a*b=3
则|a-b|=√(lal �0�5 -2a*b+lbl �0�5 ) =√10

Answer 3

|a+b|=4 两边平方可得 a^2+b^2+2ab=16 即2ab=3
(|a-b|)^2= a^2+b^2-2ab=9+4-3=10 所以|a-b|=根号10

Answer 4

|a+b|�0�5=a�0�5+2a*b+b�0�5=9+2a*b+4=13+2a*b 因为：|a+b|=4，故a*b=3/2 |a-b|�0�5=a�0�5-2a*b+b�0�5=13-2a*b=13-3=10 所以：|a-b|=√10

Answer 5

|a-b|=21