01 Key Concepts
Vector vs. Scalar
A scalar has only magnitude (like temperature or mass); a vector has both magnitude and direction (like velocity or force).
Vector Notation
Often written as an arrow over a letter, or as component form (x,y), showing horizontal and vertical parts.
Magnitude of a Vector
For a vector (x,y), magnitude = sqrt(x^2+y^2) — found using the Pythagorean theorem.
Adding Vectors
Add corresponding components: (a,b) + (c,d) = (a+c, b+d).
Scalar Multiplication of a Vector
Multiply each component by the scalar: k*(x,y) = (kx, ky), which scales the vector's length without changing its direction (unless k is negative, which reverses it).
02 Key Formulas
- Magnitude of (x,y) = sqrt(x^2+y^2)
- (a,b) + (c,d) = (a+c, b+d)
- k*(x,y) = (kx, ky)
03 Solved Examples
Example 1 Find the magnitude of the vector (3,4).
- Apply the formula: sqrt(3^2+4^2) = sqrt(9+16) = sqrt(25).
Answer: 5
Example 2 Add the vectors (2,5) and (4,-3).
- Add corresponding components: (2+4, 5+(-3)).
Answer: (6, 2)
Example 3 Multiply the vector (3,-2) by the scalar 4.
- Multiply each component by 4: (3*4, -2*4).
Answer: (12, -8)
04 Practice Questions
1Find the magnitude of (6,8).
10
2Add (1,2) and (3,4).
(4,6)
3Multiply (2,3) by scalar 5.
(10,15)
4Is temperature a scalar or a vector?
Scalar
5Is force a scalar or a vector?
Vector
📄 Vectors (Basic) — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.