Review the key concepts and skills for two-dimensional motion, including how to add and subtract vectors.
|Resultant||Sum of two or more vectors|
|Vector components||Horizontal and vertical parts of a vector|
How to add and subtract vectors
To add vectors we can use the head to tail method (Figure 1).
- Place the tail of one vector at the tip of the other vector.
- Draw an arrow from the tail of the first vector to the tip of the second vector. This new vector is the sum of the first two vectors.
Subtraction of a vector is the same as adding the vector with the opposite direction (see Figure 2).
In other words, vector is the negative of vector if they have the same length, but point in opposite directions. Using this trick, the head to tail method of adding vectors works for subtraction as well.
Finding perpendicular vector components
A vector can be represented as the sum of two perpendicular vector components. To find the horizontal and vertical components, we draw a right triangle with the vector as the hypotenuse (see Figure 3). One way to choose the sides of the triangle is the following:
- The horizontal component () starts at the tail of and is parallel to the horizontal axis. The head of the horizontal component has the same horizontal position as .
- The vertical component () starts at the head of and ends at the head of the original vector. is parallel to the vertical axis.
Common mistakes and misconceptions
- A common mistake is attempting to add vectors head to head, or tail to tail. However, this approach is incorrect, and gives a different answer from adding the vectors head to tail (Figure 4).
- Some people think vectors have to be added in a particular order. Since vector math is commutative, the order does not matter.
To check your understanding and work toward mastering these concepts, check out the exercise on describing two-dimensional motion with vectors.
Want to join the conversation?
- Why is this in science?(1 vote)