Maths

Class 12

Maths · Class 12 · Chapter 10

Vector Algebra

11 lessons 92 min 2 simulations

A vector carries a size and a direction, so it can describe a displacement, a velocity or a force where a single number cannot. This chapter draws vectors as directed segments, sorts them into types, adds them by the triangle law, scales them, and writes every vector in space as xî + yĵ + zk̂ so that all of this becomes arithmetic on three numbers. It then finds the vector between two points and the point dividing a segment in a given ratio, and defines two products: the dot product, a number that measures angles and projections, and the cross product, a vector perpendicular to both factors whose length is an area.

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What the exam asks

JEE Main asks for unit vectors and direction cosines, the section formula, the angle between two vectors from a·b, projections, perpendicularity (a·b = 0), collinearity and parallelism (a × b = 0 or b = λa), |a ± b|² expansions, and areas of triangles and parallelograms from |a × b|. The scalar triple product [a b c] and a × (b × c) are outside the rationalised text but are regular JEE tools; they are in the last section. Marks go on writing a·b as a vector, on the order in a × b (b × a = −a × b), on the ½ for a triangle's area, and on the sign in the external section formula.

Lessons

11 lessons · 92 min