Students represent vectors geometrically and in Cartesian components in two dimensions, and in three dimensions where appropriate, determining their magnitude, direction, and unit vector and multiplying them by real scalars. They add and subtract vectors, resolve them into perpendicular components, and use the dot product to determine alignment, perpendicularity, and the angle between nonzero vectors. They apply these skills to two-dimensional force, displacement, velocity, and acceleration problems, interpreting resultant vectors and recognizing equilibrium when the net force is zero.
On this page:
- Master skills like “Add and subtract vectors”, “Determine vector magnitude”, and “Multiply vectors by scalars” with unlimited, free practice problems
- Download (or modify) free worksheets on Vectors you can use at home or in class with practice problems across all skills in this group including “Represent vectors geometrically”, “Determine the angle between two vectors”, “Determine the dot product of two vectors”.
- Start working on adaptive units like “Vector Notation and Operations - Intro” or “Vector Scalar Multiplication and Magnitude - Intro” that include these skills and will introduce and scaffold the skills carefully for maximum learning.
Vectors: Individual Skills
Master 7 individual skills with free practice problems. Mouseover to see the skill's practice problems. Create a free account to track your progress.
Your results
Practice 'Add and subtract vectors'
Select any skill in this group by hovering over the list above. Unlimited free practice problems, automatically graded.
Hover a skill above to start practicing.
Download/Modify Free Grade 12 'Vectors' Worksheet
Print this free 'Vectors' worksheet to practice these skills away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Add and subtract vectors
- Determine the angle between two vectors
- Determine the dot product of two vectors
- Determine vector magnitude
- Multiply vectors by scalars
- Represent vectors geometrically
- Represent vectors using Cartesian components
Units Teaching These Skills
These adaptive units introduce, teach, or reinforce skills in this group (Vectors) through scaffolded problems that grow in difficulty as concepts are understood.