Question #89959

1 Answer
Mar 22, 2017

Answer:

The angle is #=41#º

Explanation:

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