Key relationship
A = Aₓ î + Aᵧ ĵ; |A| = √(Aₓ² + Aᵧ²); û = A / |A| for |A| > 0.
Physics · Class 11
Vector & unit vector
A scalar has magnitude only. A vector also has a direction. Temperature is a scalar; displacement is a vector. Rotating a vector can preserve its magnitude while changing its components. The unit vectors î and ĵ select the positive coordinate directions.
Open the interactive experiment →A vector needs size and direction.
திசையிலி அளவுக்கு எண் மதிப்பு மட்டும் உண்டு. திசையன் அளவுக்கு எண் மதிப்பும் திசையும் தேவை. அலகுத் திசையனின் அளவு ஒன்று; பூஜ்யத் திசையனுக்குத் தனிப்பட்ட திசை இல்லை.
Key notes, relationships and model limits
Remember
A scalar has magnitude only. A vector also has a direction. Temperature is a scalar; displacement is a vector. Rotating a vector can preserve its magnitude while changing its components. The unit vectors î and ĵ select the positive coordinate directions.
Common trap
Equal magnitudes do not guarantee equal vectors. Both magnitude and direction must agree.
Model limits
A is a displacement on orthogonal axes. Angles are measured counterclockwise from +x. A unit vector is dimensionless; its teal arrow is drawn using the same 1 m coordinate guide. The zero vector has no unique direction or unit vector.
What you will learn
Distinguish scalars and vectors; read direction and magnitude; construct a unit vector.
Try the experiment
Rotate the gold displacement arrow. Compare its components with the teal unit vector. Try the zero-vector preset.
Think of it this way
Walking five metres east and five metres north covers equal distances but reaches different places. A vector records that difference.
Worked example
For A = 3î + 4ĵ m, |A| = √(9+16) = 5 m and û = 0.6î + 0.8ĵ. The unit vector carries direction without metres.
Why this matters
A magnitude tells you how far; a direction tells you where. Component methods preserve both pieces of information.
Before you start
Rectangular axes · Pythagoras · sine and cosine
Check your understanding
Which pair is enough to specify a nonzero displacement in a plane?
- Magnitude alone
- Magnitude and direction
- Temperature and mass
Read the explanation
Magnitude and direction determine a nonzero vector. Alternatively, its two rectangular components determine it.
Course connection: CBSE XI Motion in a Plane; NEET/JEE kinematics. Use the assumptions stated in each question.