If $A = < - 3, - 1 >$ $A= <-3, -1 >$ and $B = < 4, 5 >$ $B= <4, 5 >$ , what is $| | A + B | | - | | A | | - | | B | |$ $||A+B|| -||A|| -||B||$ ?

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If $A = < - 3, - 1 >$ $A= <-3, -1 >$ and $B = < 4, 5 >$ $B= <4, 5 >$ , what is $| | A + B | | - | | A | | - | | B | |$ $||A+B|| -||A|| -||B||$ ?

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Answer 1 · 2018-07-01T10:30:04

$| | A + B | | - | | A | | - | | B | | = \sqrt{17} - \sqrt{10} - \sqrt{41} \approx - 5.4423$ $||A+B|| - ||A|| - ||B|| = color(crimson)(sqrt(17)-sqrt(10)- sqrt(41) ~~ - 5.4423$

Explanation:

$A=((-3),(-1))$

$B=((4),(5))$

$A+B=((-3),(-1)) +((4),(5))=((1),(4))$

$||A+B||=sqrt((1)^2+(4)^2)=sqrt(17)$

$||A||=sqrt((-3)^2+(-1)^2)=sqrt(10)$

$||B||=sqrt((4)^2+(5)^2)=sqrt(41)$

$:.||A+B|| - ||A|| - ||B|| = color(crimson)(sqrt(17)-sqrt(10)- sqrt(41) ~~ - 5.4423$

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If $A = < - 3, - 1 >$ $A= <-3, -1 >$ and $B = < 4, 5 >$ $B= <4, 5 >$ , what is $| | A + B | | - | | A | | - | | B | |$ $||A+B|| -||A|| -||B||$ ?

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If A= <-3, -1 >A=<−3,−1>A= <-3, -1 > and B= <4, 5 >B=<4,5>B= <4, 5 >, what is ||A+B|| -||A|| -||B||||A+B||−||A||−||B||||A+B|| -||A|| -||B||?

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Explanation:

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If $A = < - 3, - 1 >$ $A= <-3, -1 >$ and $B = < 4, 5 >$ $B= <4, 5 >$ , what is $| | A + B | | - | | A | | - | | B | |$ $||A+B|| -||A|| -||B||$ ?