Mathematics (AS)·Vectors in three dimensions · NSSCAS 1.7.1
Vectors in 3D: notation & operations
Narrated lesson · press play
Vectors are about to leave the flat page and step into real space! In this lesson you will learn to locate points in three dimensions using x, y and z, and to read and write vectors in all four notations the exam uses. You will add, subtract and scale vectors row by row, see what each operation means as a picture, and master the golden rule AB = b − a. By the end, 3D vectors will feel as friendly as the 2D ones you already know.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 1.7.1):
- Use rectangular Cartesian coordinates x, y, z to locate points in three dimensions, and use all four standard vector notations: the column vector, xi + yj + zk, AB with an arrow, and bold a
- Carry out addition and subtraction of vectors and multiplication of a vector by a scalar, and interpret these operations geometrically (tip-to-tail triangles, stretching and reversing)
- Use unit vectors i, j and k, position vectors and displacement vectors, including the rule AB = b − a and the scalar-multiple test for parallel vectors
Loading your lesson…
You're watching a free 3-minute preview — create a free account to keep going.