已知|a|=6,|b|=8,<a,b>=120°,求(a+b)·(a+b), |a+b|

(a+b)·(a+b)=a^2+b^2+2a.b=6^2+8^2+2*6*8*cos120=100-48=52

|a+b|=2根号13

(a+b)·(a+b)
=a*a+2a*b+b*b
=|a|^2+|b|^2+2|a||b|cos120°
=36+64-48
=52

|a+b|^2=(a+b)·(a+b)=52
|a+b|=2*13^(1/2)

(a+b)·(a+b)=|a|^2+|b|^2+2ab=36+64+2*6*8*cos120=52

可以先算出|a+b|^2

|a+b|^2=(a+b)·(a+b)=52

所以 |a+b|=根号52=2根号13

(a+b)·(a+b)
=/a/^2 + /b/^2 + 2a.b
=36+64+6*8*2*COS120
=100+96*(-0.5)
=52

(a+b)=A
|a+b|=A的平方再开方=根号下52=2根号13

1.(a+b)(a+b)=|a||a|+2|a||b|cos120'+|b||b|=36-48+64=52 2.|a+b|=2根号13