Answer
See below
Work Step by Step
Let $||u||=1\\
||v||=2\\
||w||=3\\
=4$
a) $||u+v+w||=\sqrt \\
=\sqrt ++\\
=\sqrt ++++++++\\
=\sqrt ||u||^2++++||v||^2++++||w||^2\\
=\sqrt 1+4+5+4+4+0+5+0+9\\
=\sqrt 32\\
=4\sqrt 2$
b) $<2u-3v-w>\\
=<2u-3v-w,2u-3v-w>\\
=<2u,2u-3v-w>++\\
=<2u,2u>-<2u,3v>-<2u,w>-<3v,2u>+<3v,3v>+<3v,w>-++\\
=\sqrt 2.2-2.3-2-3.2+3.3+3.-2+3+\\
=\sqrt 4||u||^2-6-2-6+9||v||^2+3-2+3+||w||^2\\
=\sqrt 4.1-6.4-2.5-6.4+9.4+3.0-2.5+3.0+9\\
=\sqrt -19\\
=\sqrt 19i$
c) $\\
=+\\
=+++<2w,3u>+<2w,-3v>+<2w,w>\\
=3-3++2.3-2.3+2\\
=3||u||^2-3++6-6+2||w||^2\\
=3.1-3.4+5+6.5-6.0+2.9\\
=44$
