SOLUTION: Evening All. Struggling on this vectors problem. i)If a and b are perpendicular, then by writing a= �a� and b= �b� simplify the expression (a-2b).(3a+5b) ii)Show that t

Question 365047: Evening All.
Struggling on this vectors problem.
i)If a and b are perpendicular, then by writing a= �a� and b= �b� simplify the expression (a-2b).(3a+5b)
ii)Show that the vectors a=i+2j and b=4i-2j are perpendicular
iii) Find the angle theta in degrees between the vectors p=i-j-k and q=2i+j+2k
Many Thanks
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!
Struggling on this vectors problem.
i)If a and b are perpendicular, then by writing a= �a� and b= �b� simplify the expression (a-2b).(3a+5b)

Sorry I don't understand "writing a= �a� and b= �b�".  If you
can explain what that means I can help you.  Here are the others:

ii)Show that the vectors a=i+2j and b=4i-2j are perpendicular

Just show that their dot product (scalar product) is 0:

(i+2j)�(4i-2j) = (1)(4)+(2)(-2) = 4-4 = 0

iii) Find the angle theta in degrees between the vectors p=i-j-k and q=2i+j+2k

Use the formula 

           u�v 
cos(@) = ------ =
         |u||v|


 =

 =

 =  =  =  =  = 

So @ = 101.1� approximately

Edwin

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