What a column vector means, and how to add, subtract and multiply vectors by a number.
What you will learn
- Read and write a column vector
- Add and subtract column vectors
- Multiply a vector by a number
- Translate a point by a vector
Across, then up
A column vector has two numbers stacked.
The top number is the movement across (positive is right, negative is left). The bottom number is the movement up or down (positive is up). A vector has a size and a direction, but no fixed starting point.
The vector 3−2 means 3 right and 2 down.
Bold letters such as <b>a</b> name vectors. When you write by hand, underline them.
To read a vector drawn on a grid, count from its tail (the start) to its head (the arrow end): across first, then up or down. To translate a point by a vector, add the top number to x and the bottom number to y.
The rest of this lesson and its 8 practice questions are locked.
In this lesson
- Across, then up
- Working with column vectors
- Try it: First question
8 practice questions, marked as you go; about 20 minutes in all.
Key terms
Scalar, Equal
In this unit: Vectors
Column vectors and how to add, subtract and multiply them, vectors between points, and vector geometry and proof in terms of a and b.
- Column vectors
- Vectors between points
- Vectors in shapes
- Vector proof