What is the angle between #<-4,2,-1 > # and #<-8,0,0> #?

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Answer 1 · 2017-03-02T07:32:08

The angle is #=29.2#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=〈-4,2,-1〉.〈-8,0,0 〉 = 32#

The modulus of #vecA#= #∥〈-4,2,-1〉∥=sqrt(16+4+1)=sqrt21#

The modulus of #vecB#= #∥〈-8,0,0〉∥=sqrt64=8#

So,

#costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=32/(sqrt21*8)=0.87#

#theta=29.2#º