Let `veca,vecb and vecc` be three vectors such that `vecane0, |veca|=|vecc|=1,|vecb|=4and |vecbxxvecc|=sqrt15`. If `vecb-2vecc=lambdaveca` then find the value of `lambda` .

Explanation

Let the angle between `vecb and vecc be alpha`. Then
`|vecbxxvecc|=sqrt15`
`|vecb||vecc| sinalpha=sqrt15`
`sin alpha=sqrt15/4`
` cos alpha = 1/4`
`Rightarrowvecb-2vecc=lambdaveca`
`or|vecb-2vecc|^(2)=lambda^(2)|veca|^(2)`
`|vecb|^(2)+4||vecc|^(2)-4.vecb.vecc=lambda^(2)|veca|^(2)`
`or 16+ 4 -4 xx 4xx 1 xx 1/4=lambda^(2)`
`or lambda^(2)=16 or lambda = +-4`