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Find the angle (in degrees) between the vectors. (Round your answer to two decimal places.)

Find the angle (in degrees) between the vectors. (Round your answer to two decimal-example-1
User Bialpio
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1 Answer

3 votes

You have to use the following formula to calculate the angle between TWO vectors:


\cos \left(\theta \right)\:=\frac{\vec{a\:}\cdot \vec{b\:}}{\left|\vec{a\:}\right|\cdot \left|\vec{b\:}\right|}

In this case the vector u will be the vector a, and the vector v will be the vector b

To replace the formula, we have to know the dot product:

In this case a * b

Multiply each i and each j


\vec{a\:}\cdot\vec{b\:}=\text{ \lparen}ai*bi)+(aj*bj)
\vec{a\:}\cdot\vec{b\:}=\text{ \lparen}3*-7)+(4*5)=-21+20=-1

Now


|a|=√(ai^2+aj^2)=√(3^2+4^2)=√(25)=5
|b|=√(bi^2+bj^2)=√((-7)^2+5^2)=√(74)

Now replace in


\cos(\theta)=\frac{\vec{a}\vec{b}}{\lvert\vec{a}\rvert\lvert\vec{b}\rvert}
\cos \left(θ\right)=-(1)/(5√(74))

Clear Cos with ArcCos


θ=\arccos\left(\cos\left(θ\right)\right)=\arccos\left(-(1)/(5√(74))\right)

ANS:


θ=\text{ 91.33221985\degree}

User Milan Adamovsky
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