SOLUTION: Find the angle between the vectors
[-5]and [2]
[ 3] [4]
theta arc cos (-13over square root 225 square root 64)
I don't know what to do to finish this off.
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Question 191763This question is from textbook saxon algebra2
: Find the angle between the vectors
[-5]and [2]
[ 3] [4]
theta arc cos (-13over square root 225 square root 64)
I don't know what to do to finish this off.
This question is from textbook saxon algebra2
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To calculate the angle 
between the vectors 
and 
use this formula:
=\frac{\v{a}\cdot\v{b}}{\left|\v{a}\right|\left|\v{b}\right|})
where 
is the dot product of vectors "a" and "b", 
is the magnitude (ie length) of vector 
, and 
is the magnitude (ie length) of vector 
Note: I'm assuming you are familiar with these concepts.
So...
=\frac{-5*2+3*4}{sqrt{-5*-5+3*3}sqrt{2*2+4*4}}=\frac{-10+12}{sqrt{25+9}sqrt{4+16}}=\frac{2}{sqrt{34}sqrt{20}}=\frac{2}{sqrt{680}})
Now we have this equation:
=\frac{2}{2sqrt(170)})
Now take the arccosine of both sides to isolate 
\right)=\cos^{-1}\left(\frac{2}{2sqrt(170)}\right))
}\right)=\cos^{-1}\left(0.076696498884737\left)=1.49402443552512)
So
radians
Note: The angle in degrees is approximately:
*\frac{180}{\pi}=85.6012946450045)
Or simply
degrees
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[-5]and[2]
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