If $A = < - 7, 6 >$ $A= <-7, 6 >$ and $B = < - 3, 8 >$ $B= <-3, 8>$ , what is $| | A + B | | - | | A | | - | | B | |$ $||A+B|| -||A|| -||B||$ ?

Question

1424 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-01T03:57:34

$| | A + B | | - | | A | | - | | B | | = \sqrt{296} - \sqrt{85} - \sqrt{73}$ $||A+B||-||A||-||B||=sqrt296-sqrt85-sqrt73$

$≅ - 0.56$ $~=-0.56$ .

# A=<-7,6>, B=<-3,8>

$\Rightarrow | | A | | = \sqrt{{(- 7)}^{2} + 6^{2}} = \sqrt{49 + 36} = \sqrt{85}$ $rArr ||A||=sqrt{(-7)^2+6^2}=sqrt(49+36)=sqrt85$ , and,

$| | B | | = \sqrt{9 + 64} = \sqrt{73}$ $||B||=sqrt(9+64)=sqrt73$ >.

$A + B = < - 7 - 3, 6 + 8 >$ $A+B=<-7-3,6+8>$ = $< - 10, 14 >$ $<-10,14>$

$:. ||A+B||=sqrt(100+196)=sqrt296$ .

Hence, $||A+B||-||A||-||B||=sqrt296-sqrt85-sqrt73$

$~=17.20-9.22-8.54=-0.56$ .

If A= <-7, 6 >A=<−7,6>A= <-7, 6 > and B= <-3, 8>B=<−3,8>B= <-3, 8>, what is ||A+B|| -||A|| -||B||||A+B||−||A||−||B||||A+B|| -||A|| -||B||?