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. `sqrt29` units
B. `sqrt31` units
C. `sqrt37` units
D. `sqrt41` units

Answer

A

Explanation

`vecv=|(hati,hatj,hatk),(1,-2,2),(0,4,-3)|`
`vecv=hati[6-8]+hatj[0+3]+hatk[4-0]`
`vecv=-2hati+3hatj+4hatk rArr |vecv|=sqrt29` units.