Question #89959

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Answer 1 · 2017-03-22T09:28:57

The angle is $=41$ º

The angle between $vecA$ and $vecB$ is given by the dot product definition.

$vecA.vecB=∥vecA∥*∥vecB∥costheta$

Where $theta$ is the angle between $vecA$ and $vecB$

The dot product is

$vecA.vecB=〈2,3,1〉.〈4,1,2〉=8+3+2=13$

The modulus of $vecA$ = $∥〈2,3,1〉∥=sqrt(4+9+1)=sqrt14$

The modulus of $vecB$ = $∥〈4,1,2〉∥=sqrt(16+1+4)=sqrt21$

So,

$costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=13/(sqrt14*sqrt21)=0.758$

$theta=41$ º