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Exercise 7.5 Solution FSc 2nd Year Math

Level: F.Sc (Pre-Engg)
Class: 2nd Year
Board: Punjab Textbook Board
Subject: Mathematics
Chapter No.7: Vectors
Exercise: 7.5
Type: Solution Notes
Author: Prof. Ahmad Ali
Pages: 13
PDF Size: 6.02 MB

In this exercise we will read these topics:

  • 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.

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Exercise 7.5 Solution FSc 2nd Year Math

Exercise 7.4 Solution FSc 2nd Year Math

Level: F.Sc (Pre-Engg)
Class: 2nd Year
Board: Punjab Textbook Board
Subject: Mathematics
Chapter No.7: Vectors
Exercise: 7.4
Type: Solution Notes
Author: Prof. Ahmad Ali
Pages: 16
PDF Size: 7.55 MB

In this exercise we will read these topics:

  • 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.

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Exercise 7.4 Solution FSc 2nd Year Math

Exercise 7.3 Solution FSc 2nd Year Math

Level: F.Sc (Pre-Engg)
Class: 2nd Year
Board: Punjab Textbook Board
Subject: Mathematics
Chapter No.7: Vectors
Exercise: 7.3
Type: Solution Notes
Author: Prof. Ahmad Ali
Pages: 13
PDF Size: 6.27 MB

In this exercise we will read these topics:

  • 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.

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Exercise 7.3 Solution FSc 2nd Year Math

Exercise 7.2 Solution FSc 2nd Year Math

Level: F.Sc (Pre-Engg)
Class: 2nd Year
Board: Punjab Textbook Board
Subject: Mathematics
Chapter No.7: Vectors
Exercise: 7.2
Type: Solution Notes
Author: Prof. Ahmad Ali
Pages: 12
PDF Size: 5.88 MB

In this exercise we will read these topics:

  • 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.

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Exercise 7.2 Solution FSc 2nd Year Math

Exercise 7.1 Solution FSc 2nd Year Math

Level: F.Sc (Pre-Engg)
Class: 2nd Year
Board: Punjab Textbook Board
Subject: Mathematics
Chapter No.7: Vectors
Exercise: 7.1
Type: Solution Notes
Author: Prof. Ahmad Ali
Pages: 12
PDF Size: 5.86 MB

In this exercise 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.

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