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Let vec a , vec ba n d vec c be three v...

Let ` vec a , vec ba n d vec c` be three verctors such that ` vec a!=0,| vec a|=| vec c|=1,| vec b|=4` and `| vec bxx vec c|=sqrt(15)dot` If ` vec b-2 vec c=lambda vec a ,` then find the value of `lambda`

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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`
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