Physics

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1)

If `A =3.0*hati +4.0*hatj-2.0*hatk`

and `B =4.0*hati -3.0*hatj+5.0*hatk`

then `A xx B =|[hati,hatj,hatk],[3,4,2],[4,-3,5]|=5*4*hati +2*4*hatj -3*3*hatk -4*4*hatk+3*2*hati-3*5*hatj =`

`=26*hati -7*hatj-25*hatk= <26,-7,-25>`

Answer: the vectorial product of A and B is <26,-7,-25>

2) The figure is attached below. From the figure the angle between the position vector and the linear momentum is

`beta = 45+(180-alpha) `

where `tan(alpha) = y/x =3.1/2 rArr alpha =57.17 degree`

`beta =45+180-57.17 =167.83 degree`

The position vector of the object is

`r=sqrt(x^2+y^2) =sqrt(2^2+3.1^2) =3.69 m`

The magnitude of the angular momentum is thus

`|L| =|r xx p| =r*p*sin(beta) =r*(m*v)*sin(beta) =`

`=3.69*(1.4*4.62)*sin(167.83) =5.03 ((kg*m^2)/s)`

Answer: the magnitude of the angular momentum is `5.03 ((kg*m^2)/s)`

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