Scalar and Vector Quantities
Aim: Resolve, add and subtract vectors in one plane
A scalar is any quantity with a magnitude, but no direction.
A vector is any quantity with both magnitude and direction.
Vectors can be represented as follows to distinguish between the two:
Vectors are represented by a line with an arrow:
Length= magnitude; angle = direction
Expressed in full circle bearing (true bearing), a clockwise angle from north
Expressed as a quadrant bearing, the angle between two cardinal directions and the line
It is possible to represent a vector by splitting it into two perpendicular components. (Usually vertical and horizontal).
Multiplying a vector multiples the magnitude but does not change the direction.
If multiplied by a negative, the direction is reversed.
- Draw a reference frame
- Draw the first vector
- Draw the second vector, so that the start of the second vector is the head of the first
- Repeat for all n vectors
- Draw the resultant vector from the tail of the first vector to the head of the last one.
Note that this should be to scale.
- Calculate the perpendicular components of each vector
- Add similar components of the different vectors (add horizontal to horizontal etc.)
- Using the new values, draw a vector diagram
- Use Pythagoras and trigonometry to determine the resultant vector
Subtracting by a vector is the same as adding its negative.
vector subtraction = fa – fb
= fa + (-fb)
- Flip the vector you are subtracting by. Magnitude remains the same, but direction is reversed
- The rest is the same as vector addition