Lesson Plan Math Class 12 Ch-11 | Three Dimensional Geometry

E-LESSON PLAN MATHEMATICS
CLASS - XII
CH - 11 three DIMENSIONAL GEOMETRY

Lesson Plan, Class XII Subject Mathematics, chapter 11, Three Dimensional Geometry , for Mathematics Teacher. Effective way of Teaching Mathematics.  E lesson planning for mathematics.

Rmb dav centnary public school Nawanshahr
NAME OF THE TEACHER				DINESH KUMAR
CLASS	10+2	CHAPTER	11	SUBJECT	MATHEMATICS
TOPIC	THREE DIMENSIONAL GEOMETRY			DURATION : 20 CLASS MEETINGS

PRE- REQUISITE KNOWLEDGE:-

• Knowledge of simple concepts of trigonometry , geometry and algebra.

• Knowledge of coordinate geometry class X.

• Knowledgeof vector algebra class XII chapter 10

TEACHING AIDS:- 

Green Board, Chalk,  Duster, Charts, smart board, projector, laptop etc.

METHODOLOGY:  

Lecture snd demonstration method

LEARNING OBJECTIVES:

• Direction ratios and direction cosines of a line joining two points.

• Cartesian and vector equation of a line.

• Coplanar and skew lines.

• Angle between two lines. 

• Conditions at which two lines are parallel and perpendicular.

• Shortest distance between two lines. 

• Shortest distance between two parallel lines.

LEARNING  OUTCOMES:

After studying this lesson students should know the 

• Direction angles, direction cosines and direction ratios of a line joining two points.

• Equation of line passing through one point.

• Equation of line passing through two points.

• Angle between two lines.

• Parallelism and perpendicularity condition of two lines.

• Shortest distance between two lines.

• Coplanerity condition of lines.

RESOURCES

• NCERT Text Book,

• NCERT Exemplar Book of mathematics,

RESOURCE MATERIAL : 

• Worksheets , E-content, Basics and formulas from  (cbsemathematics.com)

KEY WORDS :

Direction angles, direction ratios, direction cosines, vector, cartesian, coplanarity conditions, skew lines.

PROCEDURE :

Start the session by asking the questions related to the scalar and vector quantities, their scalar product, vector product and their scalar triple product. Now introduce the topic Three dimensional geometry  step by step as follows.

[For Complete explanation]

Define direction angles, cosines and direction ratios. Explain the concept  by taking an example of a general vector.

Direction angles: 

These are the angles made by the vector with the positive direction of the axis. These are denoted by α, β, 𝜸

Direction cosines: 

Cosines of the direction angles are called direction cosines.

If α, β, 𝜸 are the direction angles made by a vector with the axis then cosα, cosβ, cos𝜸 are called the direction cosines. These are also denoted by l, m, n

l = cosα,  m = cosβ,  n = cos𝜸

If l, m, n are the direction cosines of a line then   l² + m² + n² = 1

Direction ratios: 

The terms which are proportional to the direction cosines are called direction ratios. These are denoted by  (a, b, c)

For Example: 

Let any vector given by : 

Its magnitude is given by 

(a, b, c) are the direction ratios and the direction cosinesl, m, n  are given by 

If  ɑ, 𝛃, 𝛄 are the direction angles made by the line with positive direction of x-axis, y-axis, z-axis then cosɑ , cos𝛃 , and cos𝛄 are called the direction cosines of that line. These are also be denoted by l, m, n such that 

Equation of a line in space.

Case I : Equation of a line passing through the point A(x₁, y₁, z₁) and is parallel to vector b is given by

In vector form equation of line is  

Where: 

In cartesian form

Case II : Equation of a line passing through the two points.

Let given equation passes through the two points A(x₁, y₁, z₁) and B(x₂, y₂, z₂). Let P(x, y, z) is any arbitrary point on the line.

Then equation of line  is given by 

In vector form equation of line is:      

Where: 

In cartesian form equation of line is

Angle between two lines

In Vector form let equations are

 

 

If two lines in space intersect each other then shortest distance between them =0, If two lines in one plane are parallel then shortest distance is the perpendicular distance between them.

Skew lines:- In space there are lines which are neither parallel nor intersecting such lines are non-coplanar and are called skew lines. 

 

Coplanar lines:- When two lines are parallel then they are called coplanar 

 

Plane:- A plane is determined uniquely if any one of the following is known. a) When normal to the plane and its distance from the origin is given. That is equation of the plane in Normal form.

b) When it passes through a point and is perpendicular to the given direction.

c) It passes through the three non- collinear points.

Coplanarity of two lines

STUDENTS DELIVERABLES:

 Review questions given by the teacher. Students should prepare the presentation on different equations of line and plane in vector and Cartesian form. Solve NCERT problems with examples.

EXTENDED LEARNING:-

Students can extend their learning in Mathematics through the RESOURCE CENTRE

Students can also find many interesting topics on mathematics at cbsemathematics.com

ASSESSMENT TECHNIQUES:-

• Assignment sheet will be given as home work at the end of the topic. 

• Separate sheets which will include questions of logical thinking and Higher order thinking skills will be given to the above average students.

• Class Test , Oral Test , worksheet and Assignments. can be made the part of assessment.

• Re-test(s) will be conducted on the basis of the performance of the students in the test.

Competency based assessment can be taken so as to ensure if the learning outcomes have been achieved or not. e.g.

• Puzzle

• Quiz

• Misconception check

• Peer check

• Students discussion

• Competency Based Assessment link: M C Q

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