`veca and vecc` are unit vectors and `|vecb|=4` the angle between `veca and vecb is cos ^(-1)(1//4) and vecb - 2vecc=lambdaveca` the value of `lambda` is

Options

A. `3,-4`
B. `1/4,3/4`
C. `-3,4`
D. `-1//4,3/4`

Answer

a

Explanation

` vecb - 2vecc = lambda veca`
` or vecb = 2vecc + lambda veca`
` or |vecb|^(2) = |2vecc + lambdaveca|^(2)`
`Rightarrow 16 = 4 |vecc|^(2) + lambda^(2)|veca|^(2) + 4lambda veca.vecc`
` = 4 + lambda^(2) + 4lambda 1/4`
`or lambda^(2) + lambda - 12 =0`
`or lambda = 3, -4`