question :the diagram shows vectors a and b if |a| = 5 , |b|=4 and a.(a+b)=36, find the size of the acute angle (feeta) between a andb

past paper 2003 paper 2 question 9

i know the formula to get cos(feeta) but dont know how to find a.b from those numbers, i know how i would normally get them....pleaase help

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# vectors?

Started by seren, May 19 2009 02:10 PM

1 reply to this topic

### #1

Posted 19 May 2009 - 02:10 PM

### #2

Posted 19 May 2009 - 02:37 PM

so we know: a . b = |a||b|cos(theta) and a.(a+b) =36

if we expand a.(a+b) =36 we get (a.a)+(a.b) =36,

a.a = 5x5xcos(0) = 25 since cos(0) =1 so 25 + (a.b) =36 therefore a.b =11

a.b = |a||b|cos(theta) ---> 11 = 5 x 4 x cos(theta)

thefore 11=20cos(theta)

theta = inverse cos(11/20)

theta = 56

if we expand a.(a+b) =36 we get (a.a)+(a.b) =36,

a.a = 5x5xcos(0) = 25 since cos(0) =1 so 25 + (a.b) =36 therefore a.b =11

a.b = |a||b|cos(theta) ---> 11 = 5 x 4 x cos(theta)

thefore 11=20cos(theta)

theta = inverse cos(11/20)

theta = 56

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