Lesson Plan Math Class 12 Ch-10

E-LESSON PLAN MATHEMATICS
CLASS - XII
CHAPTER - 10 VECTORS

Lesson Plan, Class XII Subject Mathematics, chapter 10, vector, for Mathematics Teacher. Effective way of Teaching Mathematics. Top planning by the teacher for effective teaching in the class.

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

PRE- REQUISITE KNOWLEDGE:

Knowledge of simple concepts of trigonometry , geometry and algebra. Knowledge of coordinate geometry class X.

TEACHING AIDS:

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

METHODOLOGY:

Lecture method & Demonstration Method

LEARNING OBJECTIVES:

Vector and Scalar quantities.

Types of vectors (equal, unit, zero, negative, parallel and collinear vectors)

Position vector of a point and components of a vector.

Magnitude and direction of a vector.

Direction ratios and direction cosines of a vector.

Addition of vectors, multiplication of a vector by a scalar.

Position vector of a point dividing a line segment in a given ratio(section formula with internal and external division and mid-point formula.

Properties and applications of scalar(dot) product of two vectors, vector(cross) product of two vectors and scalar triple product of three vectors.

LEARNING OUTCOMES:

After studying this lesson students should know

scalar and vector quantities.

different types of vectors, their components, their magnitude.

scalar product of two vectors

vector product of two vectors

Scalar triple product of three vectors.

Students should know the method of finding the area of triangle and area of parallelogram by using vectors.

Students also be able to apply the section formula, mid-point formula and projection formula in different problems.

RESOURCES

NCERT Text Book,

NCERT Exemplar Book of mathematics,

RESOURCE MATERIAL :

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

KEY WORDS :

Scalar quantities, vector quantities, collinear, co-planner, direction ratio, direction cosines, co-initial,

PROCEDURE :

Start the session by asking the questions related to the quantities around us and start differentiating the quantities whether they have magnitude or direction or both. Now introduce the topic vector step by step as follows.

TOPICS AND EXPLANATION

Introduction
Introduction of vectors, definition of scalar and vector quantities and making the different lists of scalar and vector quantities around us.
Scalar: The quantities which has only magnitude are called scalar quantities, for example distance.
Vector: The quantities which has magnitude and direction both are called vector quantities, for example displacement.
Explain the different types of vectors, like equal, unit, zero, negative, parallel , co-initial and collinear vectors. Give their definitions with examples.

Method of finding unit vector
Let any vector a is given by
$\vec{a}=x\widehat{i}+y\widehat{j}+z\widehat{k}$
Magnitude of this vector is given by
$|a|=\sqrt{x^{2}+y^{2}+z^{2}}$

Now divide the given vector by its magnitude then we get a unit vector in the direction of the given vector.

$\widehat{a}=\frac{\vec{a}}{|\vec{a}|}$

$=\frac{x}{\sqrt{x^{2}+y^{2}+z^{2}}}\widehat{i}+\frac{y}{\sqrt{x^{2}+y^{2}+z^{2}}}\widehat{j}+\frac{z}{\sqrt{x^{2}+y^{2}+z^{2}}}\widehat{k}$

Explain the method of finding the position vector of a point, by giving some examples and explain the method of finding the magnitude of a vector.

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.
Direction cosines:
Cosines of the direction angles are called direction cosines.
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 $\overrightarrow{r}=a\hat{i}+b\hat{j}+c\hat{k}$
Its magnitude is given by   $|\overrightarrow{r}|=\sqrt{a^{2}+b^{2}+c^{2}}$
Where a, b, c are the direction ratios of the vector
The direction cosines of the given vector is given by
$\left ( \frac{a}{\sqrt{a^{2}+b^{2}+c^{2}}},\frac{b}{\sqrt{a^{2}+b^{2}+c^{2}}},\frac{c}{\sqrt{a^{2}+b^{2}+c^{2}}} \right )$
Explain the triangle law and parallelogram law of vector addition, also explain the different properties of vector addition.
Explain the method of multiplication of a vector with a scalar.
Explain the components of vectors along x-axis, y-axis, z-axis and explain the formation of the vector in terms of components.

Position Vector from vector A to vector B
$\overrightarrow{AB}$ = Position vector of B - Position vector of A
Position vector AB passing through the points A(x₁, y₁, z₁) and B(x₂, y₂, z₂) is given by

$\mathbf{\overrightarrow{AB}= \left (x_{2}\hat{i}+y_{2}\hat{j}+z_{2}\hat{k} \right )-\left ( x_{1}\hat{i}+ y_{1}\hat{i}+ z_{2}\hat{k} \right )$
$\mathbf{\overrightarrow{AB}= \left ( x_{2}-x_{1} \right )\hat{i}+\left ( y_{2}-y_{1} \right )\hat{j}+\left ( z_{2}-z_{1} \right )\hat{k}$

Explain the section formula for internal and external division and then explain the mid-point formula.
Explain the centroid of triangle
Product of two vectors :
Scalar or Dot product of two vectors
Scalar or dot product of two vectors, vector a and vector b is given by
$\overrightarrow{a}. \overrightarrow{b}= |\overrightarrow{a}||\overrightarrow{b}|cos\theta$

where 𝞡 is the angle between two vectors, vector a and vector b.

$\hat{i}.\hat{i}=\hat{j}.\hat{j}=\hat{k}.\hat{k}=1$

$\hat{i}.\hat{j}=\hat{j}.\hat{k}=\hat{k}.\hat{i}=0$
Two vectors are perpendicular if
$\overrightarrow{a}.\overrightarrow{b}=0$

Two vectors are parallel if
$\overrightarrow{a}.\overrightarrow{b}=|\overrightarrow{a}||\overrightarrow{b}|$
Explain the properties of scalr product
Now Explain the concept of projection of a vector on a line and
$Projection \;\; of\; \; \overrightarrow{a} \; on\; \overrightarrow{b} = \frac{\overrightarrow{a}.\overrightarrow{b}}{|\overrightarrow{b}|}$

$Projection\; \; of\; \; \overrightarrow{b}\; on\; \overrightarrow{a}\; = \frac{\overrightarrow{a}.\overrightarrow{b}}{|\overrightarrow{a}|}$
Vector Product (or cross product ) of two Vectors

Vector product of two vectors $\vec{a}\; and\; \vec{b}$ is given by   $\vec{a}\times \vec{b}=|\vec{a}||\vec{b}|sin\theta \hat{n}$

Where $\hat{n}$ is a unit vector perpendicular to both   $\vec{a}\; and\; \vec{b}$

$\left | \vec{a}\times \vec{b} \right |=\left | \vec{a} \right | \; \left | \vec{b} \right |sin\theta$
Explain the method of finding the area of parallelogram and triangle by using vector algebra. Also explain the Lagrange’s identities.

Area of Parallelogram

If $\vec{a}\; and\; \vec{b}$ are two vectors representing the adjacent sides of a parallelogram then
Area of parallelogram = $=\; |\overrightarrow{a}\times \overrightarrow{b}|$

If $\vec{a}\; and\; \vec{b}$ representing two diagonals of a parallelogram then
Area of parallelogram = $\frac{1}{2}\; |\overrightarrow{a}\times \overrightarrow{b}|$

Area of triangle
If $\vec{a}\; and\; \vec{b}$ are two vectors representing two sides of triangle then
Area of triangle =   $\frac{1}{2} \left |\overrightarrow{a}\times \overrightarrow{b} \right |$

STUDENTS DELIVERABLES:

Review questions given by the teacher.

Students should prepare the presentation on the scalar product, cross product and scalar triple product of three vectors and their applications in different problems.

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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