Answer
See below
Work Step by Step
Let $||v||=2\\
||w||=6\\
=3$
a) $||w=2v||=\sqrt \\
=\sqrt +++\\
=\sqrt ||w||^2+(-2)+(-2)+(-2)(-2)||w||^2\\
=\sqrt 36-2.3-2.3+4.4\\
=\sqrt 40$
b) $<2v+5w>\\
=<2v+5w,2v+5w>\\
=<2v,2v>+<2v,5w>+<5w,2v>+<5w,5w>\\
=<2.2+2.5+5.2+5.5\\
=\sqrt 4||v||^2+10+10+25||w||^2\\
=\sqrt 4.4+10.3+10.3+25.36+3.16\\
=\sqrt 976\\
=4\sqrt 61$
c) $<2v-w,4w>\\
=<2v,4w>+\\
=8-4||w||^2\\
=8.3-4.36\\
=-120$
