If $A = < 2, 6 >$ $A= <2 , 6 >$ and $B = < - 1, 6 >$ $B= <-1,6 >$ , what is $| | A + B | | - | | A | | - | | B | |$ $||A+B|| -||A|| -||B||$ ?

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Answer 1 · 2016-01-16T20:18:36

$| | A + B | | - | | A | | - | | B | | = 24.45$ $||A+B||−||A||−||B||=24.45$

To find the magnitude of any vector $\to V = < x, y >$ $vecV=< x,y >"$ in the standard form (its tail is at the origin), just apply the formula:
$| V | = \sqrt{x^{2} + y^{2}}$ $|V|=sqrt(x^2+y^2)$
To find the sum of two vectors $A$ $A$ and $B$ $B$ , add the x-coordinates and the y-coordinates separately.
$- --- \to A + B = < 1, 12 >$ $vec(A+B)=< 1,12>$
$| | A | | = \sqrt{2^{2} + 6^{2}} = \sqrt{40}$ $||A||=sqrt(2^2+6^2)=sqrt(40)$
$| | B | | = \sqrt{{(- 1)}^{2} + 6^{2}} = \sqrt{37}$ $||B||=sqrt((-1)^2+6^2)=sqrt(37)$
$| | A + B | | = \sqrt{1^{2} + 12^{2}} = \sqrt{145}$ $||A+B||=sqrt(1^2+12^2)=sqrt(145)$
$| | A + B | | - | | A | | - | | B | | = \sqrt{145} - \sqrt{40} - \sqrt{37}$ $||A+B||−||A||−||B||=" "sqrt(145)-sqrt(40)-sqrt(37)$
$= 24.45$ $=24.45$

If A=<2,6>A= <2 , 6 > and B=<−1,6>B= <-1,6 >, what is ||A+B||−||A||−||B||||A+B|| -||A|| -||B||?