Finding the angle between 2 vectors

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To find the angle between two vectors in 3D, use the dot product formula: a·b = |a||b|cos(θ). The angle θ can be calculated using the formula θ = arccos( (a·b) / (|a||b|) ). The dot product a·b is computed as a1b1 + a2b2 + a3b3, while the magnitude |a| is found using the square root of the sum of the squares of its components. By substituting the values of the vectors a and b into these equations, the angle can be determined. This method effectively provides the angle between the two specified vectors.
PinkFlamingo
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Could someone refresh my memory how to find the angle between 2 vectors in 3d, say:

a= 4i + j + 2k
b= -i +2j + k

Thanks!
 
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dot product

a.b = |a||b|cos (ang)
 
So how would I find the angle for the two I posted?
 
He just told you. Solve for theta and plug and chug.

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

\vec{a}\cdot\vec{b} = a_1b_1 + a_2b_2 + a_3b_3
and
|\vec{a}| = \sqrt{{a_1}^2 + {a_2}^2 + {a_3}^2}

if \vec{a} = <a_1,a_2,a_3> and likewise for b.

cookiemonster
 
Last edited:
Nice thinking Cookieman...
 
Thank you!
 
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