Vectors

Overview

Vectors let you keep track of size and direction at the same time. In kinematics, this is what makes projectile motion and two-dimensional problems manageable.

What You Need to Know

• Scalars have magnitude only. Vectors have magnitude and direction.
• Displacement, velocity, acceleration, and force are vectors.
• A vector can be added, subtracted, or resolved into perpendicular components.
• Component methods are often clearer than scale drawings when exact values are needed.

How to Work Through It

1. Sort familiar quantities into scalar and vector examples.
2. Draw vector diagrams to show addition and subtraction.
3. Resolve angled vectors into horizontal and vertical components.
4. Use components to prepare for projectile motion.

Check Your Understanding

• Why is velocity a vector but speed is a scalar?
• What does a negative component mean physically?
• When is a component method more reliable than a scale drawing?
• How can one angled velocity be replaced by two perpendicular velocities?

Common Mistakes

• Adding vector magnitudes directly when the directions are different.
• Forgetting to show direction on a vector diagram.
• Swapping sine and cosine when resolving a vector.
• Treating components as extra motion rather than as a different description of the same vector.

Next Steps

• Keep your component diagrams neat because they are the starting point for projectile questions.
• Revisit any trigonometry gaps before the next lesson.