Bonsoir,
a) [tex]\overrightarrow{u}=(4\,;1)[/tex]
b) [tex]2\overrightarrow{u}=2(4\,;1) = (2*4\,;2*1)=(8\,;2)[/tex]
c) [tex]-3\overrightarrow{u}=-3(4\,;1) = (-3*4\,;-3*1)=(-12\,;-3)[/tex]
d) [tex]\frac{1}{4}\overrightarrow{u}=\frac{1}{4}(4\,;1) = (\frac{1}{4}*4\,;\frac{1}{4}*1)=(1\,;\frac{1}{4})[/tex]
e) [tex]\overrightarrow{v}=(3\,;-4)[/tex]
f) [tex]5\overrightarrow{v}=5(3\,;-4) = (5*3\,;5*(-4))=(15\,;-20)[/tex]
g) [tex]\frac{2}{3}\overrightarrow{v}=\frac{2}{3}(3\,;-4)=(\frac{2}{3}*3\,;\frac{2}{3}*(-4))=(2\,;\frac{-8}{3})[/tex]
h) [tex]-\frac{1}{4}\overrightarrow{v}=-\frac{1}{4}(3\,;-4)=(-\frac{1}{4}*3\,;-\frac{1}{4}*(-4))=(-\frac{3}{4}\,;-1)[/tex]
i) [tex]4\overrightarrow{u}-3\overrightarrow{v}=4(4\,;1)-3(3\,;-4) = (4*4\,;4*1)-(3*3\,;3*(-4))=(16\,;4)-(9\,;-12)=(16-9\,;4-(-12))=(7\,;16)[/tex]
