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Given two vectors vecA=2hati+4hatj+5hatk...

Given two vectors `vecA=2hati+4hatj+5hatkandvecB=hati+3hatj+6veck`. Find the product `vecA.vecB` and the magnitudes of `vecAandvecB`. What is the angle between them?

Text Solution

Verified by Experts

`vecA.vecB=2+12+30=44`
Magnitude `A=sqrt(4+16+25)=sqrt45` units
Magnitude `B=sqrt(1+9+36)=sqrt46` units
The angle between the two vectors is given by
`theta=cos^(-1)((vecA.vecB)/(AB))=cos^(-1)((44)/(sqrt(45)xxsqrt46))=cos^(-1)((4)/(45.49))=cos^(-1)(0.967)`
`:.theta~=15^(@)`.
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