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` .

Answer

4

Explanation

Let angle between `vecb and vecc` is `alpha.`
`"Given, "|vecbxxvecc|=sqrt(15)" "rArr" "|vecb||vecc| sin alpha=sqrt(15)" "rArr " "sin alpha=(sqrt(15))/(4)`
`therefore" "cos alpha=sqrt(1-sin^(2)alpha)=sqrt(1-(15)/(16))=(1)/(4)`
`because " "vecb-2vecc=lambdaveca`
`rArr" "(vecb-2vecc)=lambda^(2)(veca)^(2)" "rArr" "vec(b)^(2)+4vec(c)^(2)-4vecb.vecc=lambda^(2)vec(a)^(2)`
`rArr" "16+4xx1-4(|vecv||vecc|cos alpha)=lambda^(2).1^(2)`
`rArr" "20-4=lambda^(2)" "rArr" "lambda=pm4" "rArr" "|lambda|=4`