Find a vector ` vec a` of magnitude `5sqrt(2)` making an angle of `pi/4` with `x`-axis, `pi/2` with `y`-axis and an acute angle `theta` with `z`-axis.

Explanation

Given,


`|a|=sqrt(x^2+y^2+z^2)=5sqrt(2)`


`x^2+y^2+z^2=50`



Angle made by `x` axis is `pi/4`


`cos(pi/4)=(x)/(|a|)`


`(1)/(sqrt(2))=(x)/(5sqrt(2))`


`x=5`


Angle made by `y` axis is `pi/2`


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