(Solved): At the instant the displacement of a \( 2.00 \mathrm{~kg} \) object relative to the origin is \( \ ...

At the instant the displacement of a \( 2.00 \mathrm{~kg} \) object relative to the origin is \( \vec{d}=(2.00 \mathrm{~m}) \hat{i}+(4.00 \mathrm{~m}) \widehat{j}-(3.00 \mathrm{~m}) \widehat{k} \), its velocity is \( \vec{v}=-(9.18 \mathrm{~m} / \mathrm{s}) \hat{i}+(1.61 \mathrm{~m} / \mathrm{s}) \hat{j}+(9.64 \mathrm{~m} / \mathrm{s}) \hat{k} \) and it is subject to a force \( \vec{F}=(7.42 \mathrm{~N}) \hat{i}-(4.90 \mathrm{~N}) \hat{j}+(9.61 \mathrm{~N}) \hat{k} \). Find the acceleration of the object ((a), (b) and (c) for \( \hat{i}, \widehat{j} \) and \( \hat{k} \) components respectively), the angular momentum of the object about the origin ((d), (e) and (f) for \( \hat{i}, \widehat{j} \) and \( \hat{k} \) components respectively), the torque about the origin acting on the object ((g), (h) and (i) for \( \hat{i}, \widehat{j} \) and \( \hat{k} \) components respectively), and (j) the angle between the velocity of the object and the force acting on the object.