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

`vec(v)= vec(omega) xx vec(r) = |(hat(i),hat(j),hat(k)),(1,-2,2),(0,4,-3)|= hat(i) (6- 8)- hat(j) (-3) + 4 hat(k)= -2 vec(i)+ 3 vec(j) + 4 vec(k)`
`|vec(v)|= sqrt((-2)^(2) + (3)^(2) + (4)^(2))= sqrt29` unit