Vector Algebra — Class 12 CBSE Mathematics revision notes
A 3-page visual revision sheet for Vector Algebra, written for Class 12 CBSE Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Vector Algebra in one look
magnitude and direction together, added tip to tail
A vector, defined
- notation, magnitude
a, |a| - position vector of a point (x,y,z)
r = xi + yj + zk - its magnitude
|r| = √x^2+y^2+z^2 - unit vector along a, from a itself
a = fraca|a|
Types of vectors
- Zero vector: magnitude 0, direction not defined
- Unit vector: magnitude exactly 1, direction can be anything
- Collinear vectors: parallel to the same line, whatever their magnitude or direction along it
- Equal vectors: same magnitude AND same direction, positions can differ
Addition, laws it obeys
- commutative
a+b = b+a - associative
(a+b)+c = a+(b+c) - additive identity
a+0 = a - additive inverse
a+(-a) = 0
Page 1 of 3. The full sheet, all 3 pages, opens free in the app.
What this Vector Algebra sheet covers
- A vector, defined
- notation, magnitude
- position vector of a point (x,y,z)
- its magnitude
- unit vector along a, from a itself
- Types of vectors
- Zero vector
- Unit vector
- Collinear vectors
- Equal vectors
- Adding two vectors, two pictures of the same sum
- Addition, laws it obeys
- commutative
- associative
- additive identity
- additive inverse
- Vector joining two points, and the section formula
- vector from A to B, position vectors a and b
- point dividing AB in ratio m:n, internally
- dividing AB in ratio m:n, externally
- midpoint of AB, the special case m=n
- Components and direction cosines
- a vector written in components
- direction cosines l, m, n
- they always satisfy
- Scalar (dot) product: always a number
- definition, theta the angle between them
- in components
- a vector dotted with itself
- projection of a on b
- Vector (cross) product: always a vector
- definition, the unit vector n perpendicular to both
- order matters
- any vector crossed with itself
- area of the parallelogram on a and b
- Symbols
- Cross product, magnitude, area
- Which operation do you need?
- Things to remember before the traps
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Vector Algebra the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.