- #1

- 110

- 0

(2u+v).(u-2v)

=2u.u+2u.(-2v)+v.u+v.(-2v)

Where u and v are vectors and the "." is the dot. I did some but after this im lost, how can I continue?

- Thread starter PiRsq
- Start date

- #1

- 110

- 0

(2u+v).(u-2v)

=2u.u+2u.(-2v)+v.u+v.(-2v)

Where u and v are vectors and the "." is the dot. I did some but after this im lost, how can I continue?

- #2

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 956

(2u+v).(u-2v)=2u.u+2u.(-2v)+v.u+v.(-2v) correctly. Now just

combine 2u.(-2v)= -4 u.v and v.u which is also u.v:

This is 2(u.u)- 3 u.v- 2(v.v)

You can also use the fact that |u|= sqrt(u.u) so that

u.u= |u|

(2u+v).(u-2v)= |u|

- #3

- 110

- 0

Got it, thanks

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