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Natkirky

Member

Registered: 2006-10-17

Posts: 21

Vectors - The Scalar Product

Hi,

I am doing 1st year university algebra.  I was wondering if anyone could tell me if i have done this question correctly?

Q.  Let u and v be perpendicular vectors of lengths 1 and 2 respectively.  Evaluate (3u+v) • (u-2v).

By expanding the bracket I get

3(u.u)-5(u.v)-2(v.v)

Since u is a unit vector u.u=1 and as they are perpendicular u.v=0

Hence 3(1) - 5(0) - 8 = -5.

Is this correct i am unsure of what to do with v.v as v is of length 2 therefore not a unit vector so I just took the square of 2.

I would be grateful for any help with this.

Thanks

Bob

Administrator

Registered: 2010-06-20

Posts: 10,803

Re: Vectors - The Scalar Product

hi Natkirky

What you have done is exactly right.  Well done!  :)

v.v is size of v times size of v times cosine of 'angle between v and v' (ie cos zero = 1)

Bob

Last edited by Bob (2011-02-08 01:09:13)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Natkirky

Member

Registered: 2006-10-17

Posts: 21

Re: Vectors - The Scalar Product

Hi Bob,

Thanks a lot for your help I have a test on vectors tomorrow and that question was bothering me

Bob

Administrator

Registered: 2010-06-20

Posts: 10,803

Re: Vectors - The Scalar Product

hi Natkirky

You are very welcome.  Good luck with the test!

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob