Kinematics of a four bar linkage system

[influx]

Homework Statement

Homework Equations

N/A

The Attempt at a Solution

I have 2 (basic) questions about this system:

1) The question says that ω_AB = ω_ABk, I understand that bold indicates vectors whilst the plain text indicates a magnitude so ω_AB (magnitude) multiplied by k (direction vector) gives you the vector ω_AB. However, why do we multiply the magnitude by k (to yield the vector ω_AB) as opposed to multiplying by i or j? I'm trying to picture this in my head but struggling to.

2) Am I correct in saying that ω_AB = ω_BA? That is, does the order of the letters in the subscript of the vector matter? Does this matter for magnitudes (e.g. ω_AB = ω_BA), vectors^ or both/neither?

 

[CWatters]

This isn't my subject really so I'm not the best person to reply but since you haven't had one...

I believe this is just another way to represent rotation called the Axis–angle representation.

https://en.wikipedia.org/wiki/Axis–angle_representation

In mathematics, the axis–angle representation of a rotation parameterizes a rotation in a three-dimensional Euclidean space by three quantities, a unit vector e indicating the direction of an axis of rotation, and an angle θ describing the magnitude of the rotation about the axis. Only two numbers, not three, are needed to define the direction of the unit vector e because its magnitude is constrained. The angle θ scalar multiplied by the unit vector e is the axis-angle vector

θ = θe

and it's scalar multiplication not ordinary or vector multiplication..
https://en.wikipedia.org/wiki/Scalar_multiplication

In an intuitive geometrical context, scalar multiplication of a real Euclidean vector by a positive real number multiplies the magnitude of the vector without changing its direction..