How do you find the magnitude of $< - 10, - 5 >$ $<-10,-5>$ and write it as a sum of the unit vectors?

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Answer 1 · 2017-10-23T01:17:47

$| ⟨ - 10, - 5 ⟩ | = 5 \sqrt{5}$ $abs( << -10, -5 >> ) = 5sqrt(5)$

$<< -10, -5 >> = -10bb(ul hat(i)) - 5bb(ul hat(j))$

The magnitude is given by the metric norm:

$abs( << -10, -5 >> ) = sqrt((-10)^2+(-5)^2)$
$" " = sqrt(100+25)$
$" " = sqrt(125)$
$" " = 5sqrt(5)$

And using standard unit vector $bb(ul hat(i))$ and $bb(ul hat(j))$ in the $x$ -direction and the $y$ -direction respectively we have:

$<< -10, -5 >> = -10bb(ul hat(i)) - 5bb(ul hat(j))$

How do you find the magnitude of <-10,-5><−10,−5><-10,-5> and write it as a sum of the unit vectors?