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)=|{:(hati,hatj,hatk),(1,-2,2),(0,4,-3):}| = hat(i)(6-8)-hat(j)(-3)+4hat(k)`
= `-2vec(i)+3vec(j)+4vec(k)`
`|vec(v)|=sqrt((-2)^(2)+(3)^(2)+4^(2))=sqrt(29)` unit .