Question

If with reference to the right handed system of mutually perpendicular unit vectors ` hat i , hat j`and ` hat k`, ` ->alpha=3 hat i- hat j , ->beta=2 hat i+ hat j-3 hat k`, then express ` ->beta`in the from ` ->beta= ->beta_1+ ->beta_2`, where ` -

Answer 1

`vecbeta_1=lambdavecalpha=lambda(3hati-hatj)`
`vecbeta_2=vecbeta-vecbeta_1=vecbeta-lambdavecalpha`
=`(2hati+hatj-3hatk)-lambda(3hati-hatj)`
=`(2-3lambda)hati+(1+lambda)hatj-3hatk`
`vecbeta_2vecalpha=0`
`(2-3lambda)3+(1+lambda)(-1)+(-3)0=0`
`5-10lambda=0`
`lambda=1/2`
`vecbeta_1=3/2hati-1/2hatj`
`vecbeta_2=1/2hati+3/2hatj-3hatk`