3D vectors can be used to model problems in mechanics involving forces and kinematics.
3D vectors and mechanics
3D vectors can be used when modelling mechanics problems in a similar way to problems with 2D vectors. Finding position vectors, parallel and scalar multiples of vectors and the magnitude of a vector can all help solve mechanics problems with 3D vectors. This topic also requires knowledge of forces and kinematics as a prerequisite.
Example 1
A stationary 3kg object, is acted upon by three forces as follows:
F1=(5i+3j−2k)N, F2=(−i−4j+k)N and F3=(6j+4k)N
Find:
a) The resultant force.
b) The magnitude of the acceleration.
c) The distance travelled in 10s.
d) The time taken to reach a velocity of 102m.s−1.
a) The resultant force is the sum of the individual forces acting: