# 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.

# 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.

# 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.

# 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.

# 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.