If $A = < - 2, 2 >$ $A= <-2, 2 >$ and $B = < 9, 4 >$ $B= <9, 4>$ , what is $| | A + B | | - | | A | | - | | B | |$ $||A+B|| -||A|| -||B||$ ?

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If $A = < - 2, 2 >$ $A= <-2, 2 >$ and $B = < 9, 4 >$ $B= <9, 4>$ , what is $| | A + B | | - | | A | | - | | B | |$ $||A+B|| -||A|| -||B||$ ?

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Answer 1 · 2016-03-19T21:37:38

$| | A + B | | - | | A - B | | = \sqrt{85} - \sqrt{125}$ $||A+B|| - ||A-B||=sqrt85-sqrt125$

Explanation:

$A + B = C$ $A+B=C$
$C_{x} = A_{x} + B_{x} = - 2 + 9 = 7$ $C_x=A_x+B_x=-2+9=7$
$C_{y} = A_{y} + B_{y} = 2 + 4 = 6$ $C_y=A_y+B_y=2+4=6$
$| | C | | = \sqrt{C_{x}^{2} + C_{y}^{2}} | | C | | = \sqrt{7^{2} + 6^{2}} = \sqrt{49 + 36}$ $||C||=sqrt(C_x^2+C_y^2)" "||C||=sqrt(7^2+6^2)=sqrt(49+36)$
$| | C | | = \sqrt{85}$ $||C||=sqrt85$

$A - B = D$ $A-B=D$
$D_{x} = A - x - B_{x} = - 2 - 9 = - 11$ $D_x=A-x-B_x=-2-9=-11$
$D_{y} = A_{y} - B_{y} = 2 - 4 = - 2$ $D_y=A_y-B_y=2-4=-2$
$| | D | | = \sqrt{D x^{2} + D y^{2}} | | D | | = \sqrt{{(- 11)}^{2} + {(- 2)}^{2}}$ $||D||=sqrt( D x^2+ D y^2)" "||D||=sqrt((-11)^2+(-2)^2)$
$| | D | | = \sqrt{121 + 4} | | D | | = \sqrt{125}$ $||D||=sqrt(121+4)" "||D||=sqrt125$
$| | A + B | | - | | A - B | | = | | C | | - | | D | |$ $||A+B|| - ||A-B||=||C||-||D||$
$| | A + B | | - | | A - B | | = \sqrt{85} - \sqrt{125}$ $||A+B|| - ||A-B||=sqrt85-sqrt125$

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If $A = < - 2, 2 >$ $A= <-2, 2 >$ and $B = < 9, 4 >$ $B= <9, 4>$ , what is $| | A + B | | - | | A | | - | | B | |$ $||A+B|| -||A|| -||B||$ ?

1 Answer

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Humanities

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If A=<−2,2>A= <-2, 2 > and B=<9,4>B= <9, 4>, what is ||A+B||−||A||−||B||||A+B|| -||A|| -||B||?

1 Answer

Explanation:

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If $A = < - 2, 2 >$ $A= <-2, 2 >$ and $B = < 9, 4 >$ $B= <9, 4>$ , what is $| | A + B | | - | | A | | - | | B | |$ $||A+B|| -||A|| -||B||$ ?