Chapter at a Glance
1. Vector – A vector is a quantity having both magnitude and direction, such as displacement, velocity, force and acceleration.
AB is a directed line segment. It is a vector AB and its direction is from A to B.
Initial Point – The point A where from the vector AB starts is known as initial point.
Terminal Point – The point B, where it ends is said to be the terminal point.
Magnitude – The distance between initial point and terminal point of a vector is the magnitude or length of the vector AB. It is denoted by | AB |or AB.
2. Position Vector – Consider a point P (x, y, z) in space. The vector OP with initial point as origin O and terminal point P, is called the position vector of point P.
3. Unit Vector – A vector whose magnitude is unity is said to be unit vector. It is denoted as aˆ. | a:. | ˆ = 1.
4. Addition of Vectors
5. Multiplication of Vector by a Scalar – Let ar be the given vector and l be a scalar, then the product of lambda and a = lambda a
6. Rectangular Components of a Vector – Consider the vector OPuuur, where P is the point (x, y, z) and OQ, OR, OS are the projections of OP on x, y and z coordinates axes respectively.
7. Vector joining two points – Let P1(x1, y1, z1) and P2(x2, y2, z2) be the two points. Then vector joining from points P1 to P2 is P P 1 2
8. Section Formula
9. (i) Projection of vector on a line – Let the vector AB makes an angle q with directed line l .
The vector p is called the projection vector of vector AB
The vector p is called the projection vector of vector AB on line l .
10. Scalar Dot Product of Two Vectors – Scalar Product of two vectors a and b
11. Vector or Cross Product of two Vectors
12. Direction Cosines
13. Direction Cosine and Direction Ratio of a Vector
Related Articles:
- NCERT Revision Notes for Class 12 (All Subjects)
- CBSE Class 12 Maths Notes (Chapter-wise PDF)
- NCERT Solutions for class 12th Mathematics Chapter 10 Vector Algebra