Express the force F1 in Cartesian vector form.

Express the force F₁ in Cartesian vector form.

Solution

 f = xi + yj + zk.

x is x component of force
y is y component of force
z is z component of force

By Considering the direction of the force
It is making 60 deg with positive y-axis and negative x-axis. and 45 deg with positive z-axis.
Cos theta(x) = x component of force/ magnitude of x.

Therefore x component = -(cos 60*400) = 200 since it is in negative direction
Similarly y component = cos 60 * 400 = 200.
z component = cos 45 * 400 = 283.
Therefore force in cartesian form is -200i+200j+283k.