Answer
See below
Work Step by Step
Let $||v||=3\\
||w||=4\\
=-2$
a)
$||v+w||=\sqrt x\\
=\sqrt +++\\
=\sqrt ||v||^2+++||w||^2\\
=\sqrt 9-2-2+16\\
=\sqrt 21$
b) $<3v+w,-2v+3w>\\
=<3v,-2v>+<3v,3w>++\\
=3+3++\\
=3(-2)+3.3+(-2)+3\\
=3.(-2)||v||^2+3.3+(-2)+3||w||^2\\
=-6.9+9.(-2)-2.(-2)+3.16\\
=-54-18+4+48\\
=-20$
c) $
=-5-2||w||^2\\
=-5.(-2)-2.16\\
=-22$
