Summary Vector Algebra Full Chapter Notes | Class 11 Maths | JEE Mains Preparation PDF

Vector Algebra Notes for JEE Mains
By Teju

■ Basic Concepts:
• A vector has both magnitude and direction.
• Position Vector: Represents the position of a point relative to origin. If P(x,
y, z), then r = xi + yj + zk.
• Equal Vectors: Have same magnitude and direction.
• Unit Vector: â = a/|a|
• Zero Vector: Magnitude = 0.
• Collinear Vectors: Parallel or anti-parallel.

✏■ Vector Operations:
1. Addition: a + b = (a■ + b■)i + (a■ + b■)j + (a■ + b■)k
2. Subtraction: a - b = (a■ - b■)i + (a■ - b■)j + (a■ - b■)k
3. Scalar Multiplication: k·a = (ka■)i + (ka■)j + (ka■)k
4. Magnitude: |a| = √(a■² + a■² + a■²)

■ Scalar (Dot) Product:
a · b = |a||b|cosθ = a■b■ + a■b■ + a■b■
Two vectors are perpendicular if a · b = 0.

■ Vector (Cross) Product:
a × b = |a||b|sinθ n■
|a × b| = area of parallelogram formed by a and b.
Formula using determinant:
a × b = |i j k|
|a■ a■ a■|
|b■ b■ b■|

■ Model Sums (with Solutions):

Q1. Find the magnitude of vector a = 3i - 4j + 12k.
Sol: |a| = √(3² + (-4)² + 12²) = √(9 + 16 + 144) = √169 = 13

Q2. If a = 2i + j + k and b = i - j + 2k, find a · b.