ADDING VECTORS

There is a difference between velocity and speed. Velocity is a vector because it has both magnitude and direction. When velocity is positive, an object moves in the positive direction, which is typically to the right or up. When velocity is negative, an object moves in the negative direction, which is typically to the left or down. Speed is a scalar because it only has magnitude. Speed describes how fast an object is moving but does not describe a direction. Speed is the absolute value of velocity. 

DOT PRODUCT

The dot product can be used to find the angle between two vectors.

VECTOR PROJECTIONS

Vector projections can also be applied in many real-world applications. They are often used in scenarios where there is an inclined plane, and sometimes trigonometry may be applied to simplify the calculation. 

• The force vector for weight is always straight downward due to gravity. 

WORK

Work is force applied over a displacement. It is a scalar that can be calculated using the dot product or trigonometry. If the force and the displacement are in the same direction, multiply the magnitudes together. This is represented by W = ||F|| ||d||. When a constant force is applied at an angle θ, the equation needed to find the work is W = ||F|| ||d|| cos θ.