A unit vector is represented as `(0.8hat(i)+bhat(j)+04hat(k))`. Hence, the value of b must be

Options

A. 0.4
B. `sqrt(0.6)`
C. 0.2
D. `sqrt(0.2)`

Answer

D

Explanation

Given, unit vector `=0.8hat(i)+bhat(j)+0.4hat(k)`
Magnitude of vector `(Asqrt(x^(2)+y^(2)+z^(2)))`
Here, `x=0.8,y=b,z=0.4`
Now,
`=sqrt((0.8)^(2)+(b)^(2)+(0.4)^(2))`
`rArr1=sqrt(0.64+b^(2)+0.16)`
`rArr1=sqrt(0.64+b^(2)+0.16)`
`rArr1=0.64+b^(2)+0.16`
`rArr1=0.80+b^(2)`
`rArrb^(2)=1-0.80`
`rArrb^(2)=0.2`
`rArrb=sqrt(0.2)`