Answer
$\sqrt 5$
$3i - j$
$i + 3j$
$4i + 2j$
$4i + 7j$
Work Step by Step
This question asks to find $|u|, u + v, u - v, 2u, 3u-2v$
Given $u = 2i + j$ and $v = i - 2j$
$u = <2, 1>$ and $v = <1, -2>$
$|u| = \sqrt {2^2 + 1^2} = \sqrt 5$
$u + v = <2 + 1, 1 + (-2)> = <3, -1> = 3i - j$
$u - v = <2 - 1, 1 - (-2)> = <1, 3> = i + 3j$
$2u = <2(2), 2(1)> = <4, 2> = 4i + 2j$
$3u - 2v = <3(2) - 2(1), 3(1) - 2(-2)> = <4, 7> = 4i + 7j$
