What is the angle between $< 5, 2, - 1 >$ $<5 , 2 , -1 >$ and $< 1, - 3, 1 >$ $< 1, -3 , 1 >$ ?

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What is the angle between $< 5, 2, - 1 >$ $<5 , 2 , -1 >$ and $< 1, - 3, 1 >$ $< 1, -3 , 1 >$ ?

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Answer 1 · 2016-03-03T16:02:13

$cos θ = \frac{< 5, 2, - 1 > \cdot < 1, - 3, 1 >}{\sqrt{5^{2} + 2^{2} + {(- 1)}^{2}} \sqrt{1^{2} + {(- 3)}^{2} + 1^{2}}} \to cos θ = \frac{5 (1) + 2 (- 3) + (- 1) 1}{\sqrt{30} \sqrt{11}} \to θ = {cos}^{- 1} (- \frac{2}{\sqrt{330}})$ $costheta=(<5,2,-1>*<1,-3,1>)/(sqrt(5^2+2^2+(-1)^2)sqrt(1^2+(-3)^2+1^2))->costheta = (5(1)+2(-3)+(-1)1)/(sqrt(30) sqrt(11))->theta=cos^-1(-2/sqrt330)$
$θ = {96.32}^{\circ}$ $theta=96.32^@$

Explanation:

To find the angle between the vectors use the formula $cos θ = \frac{a \cdot b}{| a | | b |}$ $cos theta=(a*b)/(|a||b|$ . Note that a and b are vectors and $a \cdot b$ $a*b$ is the dot product of the vectors

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What is the angle between $< 5, 2, - 1 >$ $<5 , 2 , -1 >$ and $< 1, - 3, 1 >$ $< 1, -3 , 1 >$ ?

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Explanation:

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What is the angle between <5,2,−1><5 , 2 , -1 > and <1,−3,1> < 1, -3 , 1 > ?

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What is the angle between $< 5, 2, - 1 >$ $<5 , 2 , -1 >$ and $< 1, - 3, 1 >$ $< 1, -3 , 1 >$ ?