# Vector Algebra Class 12 Notes Mathematics Chapter 10

### 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.

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

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