Answer:
[tex]|v+w|=20[/tex]
Explanation:
We are given that
|v|=11
|w|=23
|v-w|=30
We have to find the value of |v+w|
|a-b|^2=(a+b)\cdot (a+b)=a^2+b^2-2|a||b|cos\theta
Using the formula
[tex](30)^2=(11)^2+(23)^2-2(11)(23)cos\theta[/tex]
[tex]900=121+529-506cos\theta[/tex]
[tex]900-121-529=-506cos\theta[/tex]
[tex]250=-506cos\theta[/tex]
[tex]cos\theta=-\frac{250}{506}[/tex]
[tex]|a+b|^2=|a|^2+|b|^2+2a\cdot bcos\theta[/tex]
Using the formula
[tex]|v+w|^2=(11)^2+(23)^2+2(11)(23)\times (-\frac{250}{506})[/tex]
[tex]|v+w|^2=400[/tex]
[tex]|v+w|^2=(20)^2[/tex]
[tex]|v+w|=20[/tex]
