How do you find the component form and magnitude of the vector v given initial point (1,11) and terminal point (9,3)?

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Answer 1 · 2017-08-18T23:08:06

$bb(ul v) = ( (8), (-8) ) = << 8, -8 >> = 8bb(ul hat i) - 8bb(ul hat j)$

$|| bb(ul v) || = 8sqrt(2)$

Denote the given coordinates by:

$O= (0,0)$
$A = (1,11)$
$B = (9,3)$

Then the vector $bb(ul v)$ is given by:

$bb(ul v) = bb(vec(OB)) - bb(vec(OA))$
$\ \ \ = ( (9), (3) ) - ( (1), (11) )$
$\ \ \ = ( (8), (-8) )$

Alternatively, depending upon the desired notation we can also write:

$bb(ul v) = << 8, -8 >> = 8bb(ul hat i) - 8bb(ul hat j)$

And we can calculate the magnitude, using the metric norm:

$|| bb(ul v) || = sqrt((8)^2 + (-8)^2 )$
$" " = sqrt(64+64)$
$" " = sqrt(128)$
$" " = 8sqrt(2)$