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        riddles >> putnam exam (pure math) >> vectors
        
(Message started by: svs14 on Sep 18^th, 2004, 9:42pm)

Title: vectors
Post by svs14 on Sep 18^th, 2004, 9:42pm

hi. im kinda stuck on the first question on the attached file. ive asked around and most people say it doesnt make sense but im not sure myself. if someone can give me a direct answer or ways to do it ill be grateful.thanks.

Title: Re: vectors
Post by Sir Col on Sep 19^th, 2004, 4:07am

As it is your assignment, it wouldn't help to have a direct answer to all of it, but I can get your started on each part...

(a) The vector BC=-b+0.5a, so s(-b+0.5a) will be some vector in the direction of BC
So the equation of the line through BC, r1=b+s(-b+0.5a); that is, every position of a point on this line can be found by travelling from O to B, then some distance in the direction of BC, determined by the parameter, s.
(b) Now do the same thing for the line through AE to get an equation r2, with parameter, t.
(c) If Q lies on both lines, there must be some value for s and t to make r1=r2. However, as a and b are in different directions, no amount of scalar multiplication will make a=b, so separate the components.
Write the coefficients of a on LHS = coefficients of a on RHS.
Do the same for b and solve simultaneously to find s and t.
(d) Now you can find OQ. Show that OQ is parallel to OD.

Title: Re: vectors
Post by svs14 on Sep 19^th, 2004, 5:34pm

thanks that worked for me