# Unit 07: Vectors

Notes (Solutions) of Unit 07: Vectors, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You can view online or download PDF. To view PDF, you must have PDF Reader installed on your system and it can be downloaded from Software section.

- Introduction
- Geometric Interpretation of Vector
- Multiplication of Vector by a Scalar
- Addition and Subtraction of two vectors
- Position Vector
- Vector in Plane
- Properties of Magnitude of a Vector
- Another Notation for representing Vectors in Plane
- AUnit Vector in the Direction of another given Vector
- The Ratio Formula
- Vector Geometry
- Exercise 7.1
- Introduction of Vector in Space
- Concept of a Vector in Space
- Properties of Vector
- Another notation for representing Vectors in Space
- Distance between two Points in Space
- Direction Angles and Direction of a Vector
- Exercise 7.2
- The Scalar Product of Two Vectors
- Deductions of the Important Results
- Perpendicular (Orthogonal) Vectors
- Properties of Dot Product
- Analytically Expression of Dot Product $u\cdot v$
- Angle between two Vectors
- Projection of One Vector upon another Vector
- Exercise 7.3
- The Cross Product or Vector Product of two Vectors
- Derivation of useful results of Cross Product
- Properties of Cross Product
- Analytically Expression of $u\times v$
- Parallel Vector
- Area of Parallelogram
- Area of Triangle
- Exercise 7.4
- Scalar Triple Product of Vectors
- Analytically Expression of $u\cdot(v\times w)$
- The Volume of the Tetrahedron
- Application of Vectors in Physics and Engineering
- Exercise 7.5

### Erratum

- Exercise 7.1: Q(12),Part(ii): In question, point E=5j instead of 5i —
*by Abdullah Zafar (Garrison Academy Kharian Cantt) 2015/10/31 13:27*

### Solutions

- Exercise 7.1 (Handwritten) | View Online | Download PDF (307KB)

- Exercise 7.2 | View Online | Download PDF (204KB)

- Exercise 7.3 | View Online | Download PDF (173KB)

- Exercise 7.4 (Handwritten) | View Online | Download PDF (494KB)

- Exercise 7.5 (Handwritten) | View Online | Download PDF (320KB)

The following notes was written and sent by Mr. Amir Shehzad.

**Unit 07: Vectors**| Download PDF (1.4 MB)