If $A = < 3, - 5 >$ $A= <3, -5 >$ and $B = < 9, 4 >$ $B= <9, 4 >$ , what is $| | A + B | | - | | A | | - | | B | |$ $||A+B|| -||A|| -||B||$ ?

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Answer 1 · 2016-03-06T06:25:45

$| | A + B | | - | | A | | - | | B | | = \sqrt{145} - \sqrt{34} - \sqrt{97}$ $||A+B|| - ||A|| - ||B|| = sqrt145 - sqrt34 - sqrt97$

$| | A | | = \sqrt{3^{2} + {(- 5)}^{2}}$ $||A|| = sqrt{3^2 + (-5)^2}$

$= \sqrt{34}$ $= sqrt34$

$| | B | | = \sqrt{9^{2} + 4^{2}}$ $||B|| = sqrt{9^2 + 4^2}$

$= \sqrt{97}$ $= sqrt97$

$A + B = < 12, - 1 >$ $A + B = <12,-1>$

$| | A + B | | = \sqrt{12^{2} + 1^{2}}$ $||A + B|| = sqrt{12^2 + 1^2}$

$= \sqrt{145}$ $= sqrt145$

$| | A + B | | - | | A | | - | | B | | = \sqrt{145} - \sqrt{34} - \sqrt{97}$ $||A+B|| - ||A|| - ||B|| = sqrt145 - sqrt34 - sqrt97$

If A= <3, -5 >A=<3,−5>A= <3, -5 > and B= <9, 4 >B=<9,4>B= <9, 4 >, what is ||A+B|| -||A|| -||B||||A+B||−||A||−||B||||A+B|| -||A|| -||B||?