X- component of `vec(a)` is twice of its Y- component. If the magnitude of the vector is `5sqrt(2)` and it makes an angle of `135^(@)` with z-axis then the components of vector is:

Options

A. `2sqrt(3), sqrt(3), -3`
B. `2sqrt(6), sqrt(6), -6`
C. `2sqrt(5), sqrt(5), -5`
D. None of these

Answer

C

Explanation

`a_(x)=2a_(y), cos gamma=a_(z)/a=cos 135^(@)=-1/sqrt(2)`
`rArr a_(z)=-a/sqrt(2)=-(5sqrt(2))/sqrt(2)=-5`
Now `a_(x)^(2)+a_(y)^(2)=50 rArr 4a_(y)^(2)+a_(y)^(2)+25=50`
`rArr a_(y)^(2)=5 rArr a_(y)= +- sqrt(5) rArr a_(x)= +- 2sqrt(5)`