If $A = < 6, - 1 >$ $A= <6, -1 >$ and $B = < - 7, 5 >$ $B= <-7, 5 >$ , what is $| | A + B | | - | | A | | - | | B | |$ $||A+B|| -||A|| -||B||$ ?

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Answer 1 · 2016-12-02T15:31:00

The answer is $= \sqrt{17} - \sqrt{37} - \sqrt{74}$ $=sqrt17-sqrt37-sqrt74$

It is just calculating the sum and modulus of vectors.

$\to A + \to B = ⟨ 6, - 1 ⟩ + ⟨ - 7, 5 ⟩ = ⟨ - 1, 4 ⟩$ $vecA+vecB=〈6,-1〉+〈-7,5〉=〈-1,4〉$

The modulus of

$\to A + \to B = ∥ ⟨ - 1, 4 ⟩ ∥ = \sqrt{1 + 16} = \sqrt{17}$ $vecA+vecB=∥〈-1,4〉∥=sqrt(1+16)=sqrt17$

The modulus of

$\to A = ∥ ⟨ 6, - 1 ⟩ ∥ = \sqrt{36 + 1} = \sqrt{37}$ $vecA=∥〈6,-1〉∥=sqrt(36+1)=sqrt37$

The modulus of

$\to B = ∥ ⟨ - 7, 5 ⟩ ∥ = \sqrt{49 + 25} = \sqrt{74}$ $vecB=∥〈-7,5〉∥=sqrt(49+25)=sqrt74$

So,

$∥ ∥ ∥ \to A + \to B ∥ - ∥ \to A ∥ - ∥ \to B ∥ ∥ ∥$ $∥vecA+vecB∥-∥vecA∥-∥vecB∥$

$= \sqrt{17} - \sqrt{37} - \sqrt{74}$ $=sqrt17-sqrt37-sqrt74$

If A=<6,−1>A= <6, -1 > and B=<−7,5>B= <-7, 5 >, what is ||A+B||−||A||−||B||||A+B|| -||A|| -||B||?