# NCERT Solutions for Class 12 maths Chapter 10 Vector Algebra

Vector: Those quantities which have magnitude, as well as direction, are called vector quantities or vectors. Null vector or zero vector: A vector, whose initial and terminal points coincide and magnitude is zero, is called a null vector and denoted as \vec { 0 }. The scalar components of a vector are its direction ratios and represent its projections along the respective axes. The magnitude (r), direction ratios (a, b, c) and direction cosines (l, m, n) of any vector are related as l=(a/r), m=(b/r) n=(c/r). The vector sum of two coinitial vectors is given by the diagonal of the parallelogram whose adjacent sides are the given vectors. Studying the Vector Algebra of Class 12 enables the students to understand the following: Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, the addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors, the scalar triple product of vectors.