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If `a \ a n d \ c` are unit vectors and `|b|=4` . The angel between `aa n dc` is `cos^(-1)(1//4)a n d a xx b=2a xx c \ then,b-2c=lambdaadot` The value of `lambda` is

A

3,-4

B

1/4,3/4

C

`-3,4`

D

`-1//4,3/4`

Text Solution

Verified by Experts

The correct Answer is:
a
` 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`
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CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
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  9. If vec aa n d vec b are any two vectors of magnitudes 1 and 2, resp...

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  10. If vec a and vec b are any two vectors of magnitudes 2 and 3, respe...

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  11. veca, vecb and vecc are unit vecrtors such that |veca + vecb+ 3vecc|=4...

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  12. If the vector product of a constant vector vec O A with a variable...

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  13. Let vec u , vec va n d vec w be such that | vec u|=1,| vec v|=2a n d|...

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  14. If veca, vecb and vecc be three non-coplanar vectors and a',b' and c' ...

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  15. if vecalpha||( vecbetaxx vecgamma) , then ( vecalphaxxbeta).(vecalpha...

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  17. Given three vectors vec a , vec b ,a n d vec c two of which are non-c...

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