### 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