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🏹 Chapter 10 · Class 12 Maths

Vector Algebra

Vector Algebra introduces the concept of vectors and their operations, which are essential in various fields of science and engineering. This chapter covers vector addition, subtraction, and scalar multiplication.

6

Topics

~6

Board Marks

Topics Covered

6 Topics

Introduction to Vectors

• Scalar Vector • Representation of vectors

Some Basic Concepts

• Directed line Segment • Magnitude of vector • Position Vector • Direction Cosines • Direction ratios • Equal Magnitude

Types of Vectors

Zero Vector · Unit Vector · Equal Vector · Parallel Vector · Perpendicular Vector

Vector Addition

• Triangle Law • Parallelogram Law • Properties of Vector Addition • Vector Subtraction

Multiplication of Vector by a scalar

Scalar Multiplication • Component of vector •Vector joining two points • Properties of Vector Multiplication • Section Formula

Product of two Vector

• Dot product • Angle Between vectors • Projection of • Cross product

Key Formulas

Quick Reference

Magnitude of Vector

For Vector:
a = xi + yj + zk
Magnitude:
|a| = √(x² + y² + z²)

Unit Vector

Unit Vector along a:
a = a / |a|

Position vector

Position vector of a point P(x, y, z) w.r.t. origin O(0, 0, 0):
OP = xi + yj + zk

Vector Joining Two Points

Vector joining points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂):
PQ = (x₂ - x₁)i + (y₂ - y₁)j + (z₂ - z₁)k

Addition And Subtraction of Vectors

Vector Addition:
A + B = (a₁ + b₁)i + (a₂ + b₂)j + (a₃ + b₃)k
Vector Subtraction:
A - B = (a₁ - b₁)i + (a₂ - b₂)j + (a₃ - b₃)k

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