Answer
a) $\lt -2, -\frac{16}{3}\gt$
b) $\lt 24,75 \gt$
c) $\lt 11, 33\gt$
d) $\lt 34, 109\gt$
Work Step by Step
$u = \lt -3, -8\gt$
$v = \lt 8, 25\gt$
a) $\frac{2}{3}u$
$= \frac{2}{3} \lt -3, -8\gt$
$ = \frac{2}{3}(-3i -8j)$
$= \frac{-6i}{3} + \frac{-16j}{3}$
$= \lt -2, -\frac{16}{3}\gt$
b) $3v$
$= 3\lt 8, 25\gt$
$= 3(8i +25j)$
$= 24i + 75j$
$= \lt 24,75 \gt$
c) $v - u$
$= \lt 8, 25\gt - \lt -3, -8\gt$
$= (8i +25j) - (-3i -8j)$
$= 8i + 25j + 3i + 8j$
$= 11i + 33j$
$= \lt 11, 33\gt$
d) $2u + 5v$
$= 2 \lt -3, -8\gt + 5\lt 8, 25\gt$
$= 2(-3i -8j) + 5(8i +25j)$
$= -6i - 16j + 40i + 125j$
$= 34i + 109j$
$= \lt 34, 109\gt$
