What Are Vectors in Physics?
A vector is a quantity that has both magnitude and direction, unlike a scalar which has magnitude only. Vectors describe displacement, velocity, force and more — anywhere direction matters as much as size.
A vector in physics is a quantity defined by both magnitude and direction, such as velocity or force. The magnitude of a vector with components (vx, vy) is found using |V| = √(vx² + vy²).
- •Mass
- •Speed
- •Distance
- •Temperature
- •Energy
- •Displacement
- •Velocity
- •Force
- •Acceleration
- •Momentum
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Step-by-step worked examples
A vector has components vx = 3 and vy = 4. Find its magnitude.
|V| = √(vx² + vy²) |V| = √(3² + 4²) = √(9+16) = √25 |V| = 5
A displacement vector has vx = 6 m and vy = 8 m. Find the magnitude and direction (angle from x-axis).
|V| = √(6² + 8²) = √(36+64) = √100 = 10 m θ = tan⁻¹(vy/vx) = tan⁻¹(8/6) ≈ 53.1°
Two forces act on an object: 5 N east and 12 N north. Find the resultant force.
F = √(5² + 12²) = √(25+144) = √169 F = 13 N
Flashcards
Quick quiz
Q1.Which of these is a vector quantity?
Q2.A vector has vx = 6, vy = 8. What is its magnitude?
Q3.What distinguishes a vector from a scalar?
Q4.Two equal-magnitude forces act in exactly opposite directions. What is the resultant?
The full card deck, worked steps and AI-tutor support for “What Are Vectors in Physics?” are in Notek — study by hand before your exam.
Common mistakes
Adding vector magnitudes like plain numbers. — Correct: Vectors must be added component-wise or using vector addition rules — direction matters.
Treating speed and velocity as the same thing. — Correct: Speed is a scalar (magnitude only); velocity is a vector (magnitude + direction).
Ignoring the angle when combining vectors. — Correct: The resultant depends on the angle between vectors, not just their magnitudes.
Assuming a negative vector has less magnitude. — Correct: A negative sign flips direction, not magnitude — |−V| = |V|.
FAQ
What is a vector in physics?
A vector is a quantity with both magnitude and direction, such as displacement, velocity, or force.
What is the formula for a vector's magnitude?
|V| = √(vx² + vy²), derived from the Pythagorean theorem for perpendicular components.
What are examples of vectors in physics?
Velocity, acceleration, force, displacement, and momentum are all vector quantities.
How do you calculate the resultant of two vectors?
Add their x- and y-components separately, then use |V| = √(vx² + vy²) to find the resultant magnitude.