Question

If |v|= 11, |w|= 23, |v-w|= 30, find |v+w|​

Answer 1

`|v+w|=20`

Step-by-step 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

`(30)^2=(11)^2+(23)^2-2(11)(23)cos\theta`

`900=121+529-506cos\theta`

`900-121-529=-506cos\theta`

`250=-506cos\theta`

`cos\theta=-(250)/(506)`

`|a+b|^2=|a|^2+|b|^2+2a\cdot bcos\theta`

Using the formula

`|v+w|^2=(11)^2+(23)^2+2(11)(23)* (-(250)/(506))`

`|v+w|^2=400`

`|v+w|^2=(20)^2`

`|v+w|=20`