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A particle of mass 1 kg is subjected to ...

A particle of mass 1 kg is subjected to a force which depends on the position as `vec(F ) = - k (x hat(i) + y hat(j)) " kg m s"^(-2)` with k = ` " kg s"^(-2)` .At time t = 0 the particle's position `vec(r ) = (1/sqrt(2)hat(i) +sqrt(2)hat(j))` m and its velocity `vec(v ) = (-sqrt(2) hat(i) + sqrt(2) hat(j) + 2/pi hat(k)) m s^(-1)` . Let `v_(x) and v_(y)` denote the x and the y components of the particle's velocity respectively . Ignore gravity . When z = 0.5 m , the value of `(x v_(y) -y v_(x))` is ____ `m^(2)s^(-1)` .

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