Rotation is a vector having a direction and magnitude.
counterclockwise
Simply put, a vector is 2 dimensional. Think of speed - it is only one dimensional. It is not a vector, it is a scalar. It is measured in a scale, most commonly noticed when inside a vehicle. You are travelling at 100km/h (60mph) Vectors are 2 dimensional, they have a magnitude and a direction. Think of velocity, as an arrow - imagine you are travelling at 60 mph in a northerly direction, your arrow would be pointing to the notth, with a magnitude of 60mph, If you were travelling at 60mph in a southerly direction, your velocity vector would be pointing towards the south, the exact opposite of your vector if you were travelling in a northerly direction. However the speed in these two scenario's, speed not being a vector, remains exactly the same, 60mph.
1/4 of 360 degrees = 90 degrees which is a right angle
It's not. Cos(Θ) only gives you the x-component of a vector. In order to find its y-component, you also need to use sin(Θ).
The fulcrum
Angular velocity is a vector quantity that describes the rate of rotation of an object about an axis. It has both magnitude (how fast the object is rotating) and direction (the axis of rotation). Scalar angular velocity only considers the magnitude of the rotation rate without specifying the direction.
Moment arm is a scalar quantity, as it represents the perpendicular distance from the axis of rotation to the line of action of a force. It does not have a direction associated with it, unlike vectors.
A scalar times a vector is a vector.
vector
Yes, you can add a scalar to a vector by adding the scalar value to each component of the vector.
A couple is a vector quantity because it has both magnitude (related to the moment of force) and direction (related to the axis of rotation).
Scalar
When multiplying a vector by a scalar, each component of the vector is multiplied by the scalar. This operation changes the magnitude of the vector but not its direction. Similarly, dividing a vector by a scalar involves dividing each component of the vector by the scalar.
An earthquake is neither a scalar nor a vector. It is an event.
vector
vector
Yes, you can multiply a vector by a scalar. The scalar will multiply each component of the vector by the same value, resulting in a new vector with each component scaled by that value.