If $A= <6, -1 >$ and $B= <4, 5 >$ , what is $||A+B|| -||A|| -||B||$ ?

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Answer 1 · 2016-12-29T06:19:34

The answer is $=sqrt116-sqrt37-sqrt41=-1.72$

$vecA=〈6,-1〉$

$vecB=〈4,5〉$

$vecA+vecB=〈6,-1〉+〈4,5〉=〈10,4〉$

The modulus of $vecA+vecB=∥〈10,4〉∥=sqrt(100+16)=sqrt116$

The modulus of $vecA=∥〈6,-1〉∥=sqrt(36+1)=sqrt37$

The modulus of $vecB=∥〈4,5〉∥=sqrt(16+25)=sqrt41$

Therefore,

$∥vecA+vecB∥-∥vecA∥-∥vecB∥=sqrt116-sqrt37-sqrt41$

$=-1.72$

If A= <6, -1 >A= <6, -1 > and B= <4, 5 >B= <4, 5 >, what is ||A+B|| -||A|| -||B||||A+B|| -||A|| -||B||?