Homework Help: Dot product

1. Mar 15, 2013

nameVoid

find 2 unit vectors that make an angle of pi/3 with <3,4>

<3,4>dot<a,b>=5/2=3a+4b
b=5/8-3/4 a

|<a,b>|=1
such that
a^2+25/64+15/16a+9/16 a^2=1
25/16 a^2+15/16/ a=39/64
100a^2+60a=39
a^2+3/5a=39/100
(a+3/10)^2=48/100
a=(4sqrt(3)+-3)/10
so
b=5/8-(12sqrt(3)+9)/40
=(200-96sqrt(3)-72)/320
=(128-96sqrt(3))/320
=(32-24sqrt(3))/80
=(8-6sqrt(3))/20
=(4-3sqrt(3))/10
so far so good

b=5/8-(12sqrt(3)-9)/40
=(200-96sqrt(3)+72)/320
=(272-96sqrt(3))/320
=(68-24sqrt(3))/80
=(34-12sqrt(3))/40
=(17-6sqrt(3))/20 // correct me if im wrong

2. Mar 16, 2013

tiny-tim

hi nameVoid!

your method looks basically correct (but i haven't checked it)

however, it's really complicated

try first finding the vector perpendicular to (3,4) and with the same magnitude

3. Mar 16, 2013

nameVoid

The solution for b2 is incorrect by the book

4. Mar 16, 2013

tiny-tim

shouldn't it be minus 15/16 ?

5. Mar 19, 2013

nameVoid

Ah yes my mistake

6. Mar 20, 2013

HallsofIvy

Looking at <3, 4>, you should have seen that <4, -3> is perpendicular without needing to write anything!