**Level:** F.Sc (Pre-Engg)**Class:** 2nd Year**Board:** Punjab Textbook Board**Subject:** Mathematics**Total Exercises:** 5**Type:** Notes

TITLE | SOLUTION |
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Exercise 7.1 | View |

Exercise 7.2 | View |

Exercise 7.3 | View |

Exercise 7.4 | View |

Exercise 7.5 | View |

**In this chapter we will read these topics:**

- Define scalar quantity.
- Define the vector quantity.
- Give the geometrical interpretation of a vector quantity.
- Define the magnitude of a vector.
- Define unit vector.
- Define null vector.
- Define negative of a vector.
- Define the multiplication of a vector by a scalar.
- Define equal vectors.
- Define parallel vectors.
- Define triangular law of the addition of vectos.
- What is the parallelogram law of vector addition?
- Describe the subtraction of two vectors.
- Define the position vector.
- Describe vector in a plane.
- Discuss the addition and subtraction of two vectors in a plane.
- Define the magnitude of a vector in R2.
- State and prove ratio formula.
- Introduction of a vector in space.
- Discuss the addition and subtraction of two vectors in space.
- Find the magnitude, length, a norm of a vector in space.
- Properties of a vector in space.
- State and prove a commutative property of addition of vector in space.
- State and prove the associative property of addition of vectors in space.
- State and prove the additive inverse of a vector in space.
- State and prove the distributive property of a vector in space.
- State and prove scalar multiplication property of a vector in space.
- Write the form of the vector in space.
- State and prove distance formula.
- Define direction angles and direction cosines of a vector.
- Scalar product of two vectors.
- Define scalar and dot product.
- Define the scalar product of vectors in a plane.
- Define the scalar product of vectors in a space.
- Define perpendicular vectors.
- Show that the zero vector is perpendicular to every vector.
- Properties of dot product.
- Define the angle between two vectors.
- Projection of a vector upon another.
- Cross product or vector product.
- Define the cross product of two vectors.
- Define the right-hand rule.
- Important results of the cross product.
- The analytical expression of cross products.
- Properties of cross product.
- Define the area of a parallelogram.
- Define area of a triangle.
- Scalar triple product of vectors.
- Define the scalar triple product of three vectors.
- Define parallelepiped.
- Define tetrahedron.
- Give the geometrical interpretation of the scalar triple product.
- Define the volume of a tetrahedron.
- Properties of scalar triple product.
- Define coplanar lines.
- Find the volume of a tetrahedron.
- Define words done by a force.
- Define moment of arm.