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If vector 1=(2,5) and vector 2=(4,-3), what is the angle between the two vectors? Round your answer to one decimal place.

User Cina
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The dot product between two vectors is defined as


v_1\cdot v_2 = ||v_1||\cdot ||v_2||\cdot \cos(\alpha)

where
\alpha is the angle between the two vectors.

So, we deduce


\cos(\alpha) = (v_1\cdot v_2)/(||v_1||\cdot ||v_2||)

The dot product is computed as the sum of the product of correspondent coordinates:


(2,5)\cdot(4,-3) = 2\cdot 4 + 5\cdot(-3) = 8-15 = -7

whereas the norm of a vector is the square root of the sum of the squares of the coordinates:


||v_1|| = √(2^2+5^2)=√(29),\quad ||v_1|| = √(4^2+(-3)^2)=5

So, we have


\cos(\alpha) = (-7)/(5√(29)) = -0.26

This implies


\alpha = \arccos(-0.26) \approx 105

User Jingqiang Zhang
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