Aparticle moves through an xyz coordinate system while a force acts on it. when the particle has the position vector r with arrow = (2.00 m)i hat − (3.00 m)j + (2.00 m)k, the force is f with arrow = fxi hat + (7.00 n)j − (5.00 n)k and the corresponding torque about the origin is vector tau = (1.00 n · m)i hat + (0.400 n · m)j + (−0.400 n · m)k. determine fx. -i know that you have to find the vector components of f x r, and i did for j and k since i cancels out. but i keep getting the wrong answer. provide the solution and the correct answer. i only have three attempts left.

The question is incomplete, below is the complete question "A particle moves through an xyz coordinate system while a force acts on it. When the particle has the position vector r with arrow = (2.00 m)i hat − (3.00 m)j + (2.00 m)k, the force is F with arrow = Fxi hat + (7.00 N)j − (5.00 N)k and the corresponding torque about the origin is vector tau = (4 N · m)i hat + (10 N · m)j + (11N · m)k.

Determine Fx."

Explanation:

We asked to determine the "x" component of the applied force. To do this, we need to write out the expression for the torque in the in vector representation.

torque=cross product of force and position . mathematically this can be express as

Where

 and the position vector

using the determinant method to expand the cross product in order to determine the torque we have

by expanding we arrive at

since we have determine the vector value of the toque, we now compare with the torque value given in the question

if we directly compare the j coordinate we have

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min