What is the angle between #<5,7,1># and #<5,1,7> #?

1 Answer
Jan 18, 2017

The angle is #58.7#º

Explanation:

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

#vecA.vecC=∥vecA∥*∥vecB∥costheta#

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

The dot product is

#vecA.vecB=〈5,7,1〉.〈5,1,7〉=25+7+7=39#

The modulus of #vecA#= #∥〈5,7,1〉∥=sqrt(25+49+1)=sqrt75#

The modulus of #vecC#= #∥〈5,1,7〉∥=sqrt(15+1+49)=sqrt75#

So,

#costheta=(vecA.vecC)/(∥vecA∥*∥vecC∥)=39/(sqrt75*sqrt75)=39/75=0.52#

#theta=58.7#º