Class 12 Maths Vector Algebra 🔥 Chapter 10 | Introduction to Vectors | Scalars vs Vectors | Faiz Sir

Описание: 📘 VECTOR ALGEBRA – Class 12 | Chapter 10 | NCERT
🎯 Last & Complete Introductory Part
👨‍🏫 By Faiz Sir | M.Sc. Maths with CS
📌 Channel: Infinix Classes Maths

👉 इस वीडियो में Class 12 Maths के Chapter 10 – Vector Algebra का पूरा बेसिक Introduction detail में समझाया गया है।
यह वीडियो beginners के लिए बहुत important है और आगे के सभी vector chapters की strong foundation बनाता है।

👉 In this video, we discuss the complete basic introduction of Vector Algebra with clear concepts, solved examples, and exam-oriented questions as per NCERT & CBSE syllabus.

📚 Topics Covered in This Video:

✔ Introduction to Vectors
✔ Scalars vs Vectors (with real-life examples)
✔ Types of Vectors
✔ Vector Addition (Triangle & Parallelogram Law)
✔ Properties of Vector Addition
✔ Multiplication of Vector by Scalar
✔ Unit Vector
✔ Direction Ratios & Direction Cosines
✔ Vector Joining Two Points
✔ Section Formula (Internal & External Division)
✔ Collinear Vectors
✔ Important MCQs & Board Level Questions

✍️ Solved Examples & Questions Include:

🔹 Graphical representation of vectors
🔹 Classification of scalar & vector quantities
🔹 Equality of vectors
🔹 Unit vector problems
🔹 Vectors joining two points
🔹 Section formula numericals
🔹 Collinearity proofs
🔹 Direction cosines
🔹 Important CBSE objective & subjective questions

📌 This lecture is extremely useful for:
✔ CBSE Board Exams 2025
✔ School Exams
✔ Concept Building
✔ One Shot Revision
✔ Competitive Exams (Basic Level)

👉 अगर आपको Vector Algebra मुश्किल लगता है, तो यह वीडियो आपके लिए game-changer है 💯

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📘 Watch till the end for full clarity & exam confidence! 💪

VECTOR ALGEBRA | Class - 12 | Chapter – 10 | NCERT | By : FAIZ SIR
Introduction:
Types of Vectors:

Example: Represent graphically a displacement of 40 km, 30° west of south.

Example: Classify the following measures as scalars and vectors.
5 seconds
1000 cm3


Example: In Fig., which of the vectors are: (i) Collinear (ii) Equal (iii) Coinitial

Q) Classify the following as scalar and vector quantities.
(i) time period (ii) distance (iii) force(iv) velocity (v) work done

Q) Answer the following as true or false.
𝒂 ⃗ and –𝒂 ⃗ are collinear.
Two collinear vectors are always equal in magnitude.
Two vectors having same magnitude are collinear.
Two collinear vectors having the same magnitude are equal.

Addition of Vectors:
Properties of vector addition
Property 1: For any two vectors 𝒂 ⃗ and 𝒃 ⃗,
𝒂 ⃗+ 𝒃 ⃗=𝒃 ⃗+𝒂 ⃗ (Commutative property)


Property 2: For any three vectors 𝒂 ⃗, 𝒃 ⃗ 𝒂𝒏𝒅 𝒄 ⃗
(𝒂 ⃗ + 𝒃 ⃗ )+ 𝒄 ⃗= 𝒂 ⃗+(𝒃 ⃗ + 𝒄 ⃗) (Associative property)


Multiplication of a Vector by a Scalar:

Example: Find the values of x, y and z so that the vectors 𝐚 ⃗=𝐱𝐢 ̂+𝟐𝐣 ̂+𝐳𝐤 ̂ 𝐚𝐧𝐝 𝐛 ⃗=𝟐𝐢 ̂+𝐲𝐣 ̂+𝐤 ̂ are equal.

Vector joining two points:

Example: Find the vector joining the points P(2, 3, 0) and Q(– 1, – 2, – 4) directed from P to Q.

Section formula:

Example: Consider two points P and Q with position vectors (𝑶𝑷) ⃗=𝟑𝒂 ⃗−𝟐𝒃 ⃗ and (𝑶𝑸) ⃗= 𝒂 ⃗+𝒃 ⃗. Find the position vector of a point R which divides the line joining P and Q in the ratio 2:1, (i) internally, and (ii) externally.
Q) Find the values of x and y so that the vectors 𝟐𝒊 ̂+𝟑𝒋 ̂ and 𝐱𝒊 ̂+𝒚𝒋 ̂ are equal.

Q) Find the sum of the vectors 𝒂 ⃗= 𝒊 ̂−𝟐𝒋 ̂+𝒌 ̂, 𝒃 ⃗=−𝟐𝒊 ̂+𝟒𝒋 ̂+𝟓𝒌 ̂ and 𝒄 ⃗= 𝒊 ̂−𝟔𝒋 ̂−𝟕𝒌 ̂.

Q) Find the unit vector in the direction of vector (𝑷𝑸) ⃗ , where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively.

Q) Find a vector in the direction of vector 𝟓𝒊 ̂−𝒋 ̂+𝟐𝒌 ̂ which has magnitude 8 units.

Q) Show that the vectors 𝟐𝒊 ̂−𝟑𝒋 ̂+𝟒𝒌 ̂ and −𝟒𝒊 ̂+𝟔𝒋 ̂−𝟖𝒌 ̂ are collinear.

Q) Show that the vector 𝒊 ̂+𝒋 ̂+𝒌 ̂ is equally inclined to the axes OX, OY and OZ.

Q) Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are 𝒊 ̂+𝟐𝒋 ̂−𝒌 ̂ and −𝒊 ̂+𝒋 ̂+𝒌 ̂ respectively, in the ratio 2 : 1
(i) internally (ii) externally

Q) If 𝒂 ⃗ and 𝒃 ⃗ are two collinear vectors, then which of the following are incorrect:
(A) 𝒃 ⃗="λ" 𝒂 ⃗, for some scalar λ
(B) 𝒂 ⃗=±𝒃 ⃗
(C) the respective components of 𝒂 ⃗ and 𝒃 ⃗ are not proportional
(D) both the vectors 𝒂 ⃗ and 𝒃 ⃗ have same direction, but different magnitudes.