Vector: Modulus of a Vector and Arithmetic operations

Sub-topic:       Modulus of a vector

Duration:       80 minutes

Learning Objectives: By the end of the lesson, students should be able to perform simple operations on vectors.

Reference Materials:  New Further Mathematics Project 2 by M. R Tuttuh Adegun

Previous Knowledge: Students can perform arithmetic operations on vectors

Instructional Materials:  Mathematical set.

MAGNITUDE OF A VECTOR

The magnitude of a vector a, sometimes called the modulus of the vector is represented by |a|.

Zero Vector:  The zero vector is a vector with zero magnitude.

Unit Vector:  The unit vector is the vector represented by a and is such that a = |a| a

Negative Vector:     The negative vector of a is written as – a

Equality of vector:   Two vectors are equal when they have same magnitude and direction.

UNIT VECTOR

ARITHMETIC OPERATIONS ON VECTORS

Example:       If p = 2i –  3j; q =  3i + 5j and r = i + j; Find the values of

1. 2p + q + 3r
2. 3p – 2q

Solution

1. 2p = 2(2i – 3j ) = 4i – 6j

3r = 3( i + j ) = 3i + 3j

Therefore; 2p + q + 3r = (4i – 6j) + (3i + 5j) + (3i + 3j)

                                                = 10i + 2j

• 3p = 3(3i – 3j) = 9i – 9j

2q = 2(3i + 5j) =  6i + 10j

Therefore 3p – 2q = (9i – 9j) – (6i + 10j) =3i – 19j

Evaluation: New Further Mathematics Project 2, by M.R Tuttuh Adegun et al. Page 262, Exercise 14, no 5

Conclusion: Teacher summarizes the topic, marks the students’ notes, does correction and allows the students to copy.

Assignment: New Further Mathematics Project 2, by M.R Tuttuh Adegun et al. Page 262, Exercise 14, no 6