Question

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

Answer 1

Correct Answer - A
`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)+4hat(k)-2vec(I)+3vec(j)+4vec(k)`
`|vec(v)|= sqrt((-2)^(2)+(3)^(2)+(4)^(2))=sqrt(29) unit`