# If A=3i+2j+3k and B=i-j+2k then what is angel between them?

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#### Explanation

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#### Explanation:

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Mar 9, 2018

The angle is $= {52.5}^{\circ}$

#### Explanation:

The angle between $2$vectors, $\vec{A}$ and $\vec{B}$ is given by the dot product definition.

vecA.vecB=∥vecA∥*∥vecB∥costheta

Where $\theta$ is the angle between $\vec{A}$ and $\vec{B}$

The dot product is

vecA.vecB=〈3,2,3〉.〈1,-1,2〉=(3)*(1)+(2)*(-1)+(3)*(2)=7

The modulus of $\vec{A}$= ∥〈3,2,3〉∥=sqrt(9+4+9)=sqrt22

The modulus of $\vec{B}$= ∥〈1,-1,2〉∥=sqrt(1+1+4)=sqrt6

So,

costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=7/(sqrt22*sqrt6)=0.609

$\theta = \arccos \left(0.609\right) = {52.5}^{\circ}$

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