SOLUTION: Hi All, Having difficulty with this particular problem on a task sheet, any help would be greatly appreciated. Given a=i+3j-k and b=2i+j-k, find a.b and the cosine of t

Algebra ->  Length-and-distance -> SOLUTION: Hi All, Having difficulty with this particular problem on a task sheet, any help would be greatly appreciated. Given a=i+3j-k and b=2i+j-k, find a.b and the cosine of t      Log On


   

Question 364633: Hi All,
Having difficulty with this particular problem on a task sheet, any help would be greatly appreciated.
Given a=i+3j-k and b=2i+j-k, find a.b and the cosine of the angle Theta between the vectors
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the dot product because,
a%2Ab=abs%28a%29abs%28b%29cos%28theta%29
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a%2Ab=a%5B1%5D%2Ab%5B1%5D%2Ba%5B2%5D%2Ab%5B2%5D%2Ba%5B3%5D%2Ab%5B3%5D
a%2Ab=1%282%29%2B3%281%29%2B%28-1%29%28-1%29=2%2B3%2B1=highlight%286%29
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abs%28a%29=sqrt%281%5E2%2B3%5E1%2B%28-1%29%5E2%29=sqrt%281%2B9%2B1%29=sqrt%2811%29
abs%28b%29=sqrt%282%5E2%2B1%5E2%2B%28-1%29%5E2%29=sqrt%284%2B1%2B1%29=sqrt%286%29
cos%28theta%29=a%2Ab%2F%28abs%28a%29%2Aabs%28b%29%29=6%2F%28sqrt%2811%29sqrt%286%29%29
cos%28theta%29=%286%2Asqrt%2866%29%29%2F66=sqrt%2866%29%2F11
cos%28theta%29=0.7385
highlight%28theta=42.4%29degrees