Question

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

Answer 1

Answer:

$|v+w|=20$

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

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

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

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

$250=-506cos\theta$

$cos\theta=-\frac{250}{506}$

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

Using the formula

$|v+w|^2=(11)^2+(23)^2+2(11)(23)\times (-\frac{250}{506})$

$|v+w|^2=400$

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

$|v+w|=20$