What is the angle between $<5,4,3 >$ and $< 1,-5,-7 >$ ?

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Answer 1 · 2017-01-31T13:40:49

The angle is $126$ 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

$vecA.vecB=〈5,4,3〉.〈1,-5,-7〉=5-20-21=-36$

The modulus of $vecA$ = $∥〈5,4,3〉∥=sqrt(25+16+9)=sqrt50$

The modulus of $vecB$ = $∥〈1,-5,-7〉∥=sqrt(1+25+49)=sqrt75$

So,

$costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=-36/(sqrt50*sqrt75)=-0.588$

$theta=126$ º

What is the angle between <5,4,3 > <5,4,3 > and < 1,-5,-7 >< 1,-5,-7 >?