The linear velocity of a particle on a rotating body is given by `vec v = vec omega xx vec r" where "vec omega` is the angular velocity and `vec r` is the radius vector. What is the value of |v| if `vec omega = hati -2hatj+2hatk and vec r =4hatj-3hatk` ?

Options

A. `sqrt(23)` units
B. `sqrt(29)` units
C. `sqrt(35)` units
D. `sqrt(47)` units

Answer

B

Explanation

`vec v = vec omega xx vec r`
`=|{:(hati, hatj, hatk),(1,-2,2),(0,4,-3):}|`
`=hati (+6-8)+hatj[0-(-3)]+hatk (4-0)`
`vec v =-2hati +3hatj +4hatk`
`therefore |v| = sqrt ((-2)^(2)+(3)^(2)+(4)^(2))= sqrt (29)` units