The linear velocity of a rotating body is given by `vec(v)=vec(omega)xxvec(r)`, where `vec(omega)` is the angular velocity and `vec(r)` is the radius vector. The angular velocity of a body is `vec(omega)=hat(i)-2hat(j)+2hat(k)` and the radius vector `vec(r)=4hat(j)-3hat(k)`, then `|vec(v)|` is-

Options

A. `sqrt(29)` units
B. `sqrt(31)` units
C. `sqrt(37)` units
D. `sqrt(41)` units

Answer

A

Explanation

`vec(v)=vec(omega)xxvec(r)=|(hat(i),hat(j), hat(k)),(1,-2,2),(0,4,-3)|`
`=hat(i)(6-8)-hat(j)(-3)+hat(k)(4)=-2hat(i)+3hat(j)+4hat(k)`
`|vec(v)|=sqrt(2^(2)+3^(2)+4^(2))=sqrt(4+9+16)=sqrt(29)`