Answer:
vec(F) = [ -40.193 i + 17.101 j + 24.317 k ]
Explanation:
Given:
-The force P = 50.0 N
- Angle with x-axis α = 143.5
- Angle with y-axis β = 70.0
- Angle with z-axis γ = 60.9
Find:
Find the Cartesian components of force P acting in the x, y, and z directions,
Solution:
- The Force vector in the Cartesian coordinate system is given by the dot product of the Force P and the unit vector in its direction.
F.unit(u) = vec(F)
- Where, the unit vector is defined as:
unit (u) = [ cos(α) i + cos(β) j + cos(γ) k ]
- Using the given unit angles α , β, and γ compute unit (u):
unit (u) = [ cos(143.5) i + cos(70) j + cos(60.9) k ]
unit (u) = [ -0.80386 i + 0.34202 j + 0.48634 k ]
- The force vector is:
vec(F) = 50.[ -0.80386 i + 0.34202 j + 0.48634 k ]
vec(F) = [ -40.193 i + 17.101 j + 24.317 k ]
