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Vector Algebra — Flashcards

Madhya Pradesh Board · Class 12 · Mathematics

52 flashcards for Vector Algebra (Madhya Pradesh Board Class 12 Mathematics) to test yourself on key terms and facts.

117 questions52 flashcards15 formulas & key relations5 concepts

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A comparison chart illustrating the key differences between scalar and vector quantities, providing examples for each.
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52 Flashcards·
अदिश और सदिश राशियाँScalar and vector quantitiesPosition vector magnitudeस्थिति सदिश का परिमाणसदिश का अवयवी रूपComponent form of a vectorUnit vectorएकक सदिश
Card 1अदिश और सदिश राशियाँ

इन राशियों को अदिश या सदिश के रूप में वर्गीकृत करें: 5 seconds, 10 Newton, 30 km/hr, 10 g/cm³, उत्तर की ओर 20 m/s.

Answer

चरण 1: एक अदिश में केवल परिमाण होता है। एक सदिश में परिमाण और दिशा होती है। चरण 2: 5 seconds → अदिश। चरण 3: 10 Newton → सदिश। चरण 4: 30 km/hr → अदिश। चरण 5: 10 g/cm³ → अदिश। चरण 6: उत्तर की ओर 20 m/s …

Card 2Scalar and vector quantities

Classify these quantities as scalar or vector: 5 seconds, 10 Newton, 30 km/hr, 10 g/cm³, 20 m/s towards north.

Answer

Step 1: A scalar has magnitude only. A vector has magnitude and direction. Step 2: 5 seconds → scalar. Step 3: 10 Newton → vector. Step 4: 30 km/hr → scalar. Step 5: 10 g/cm³ → scalar. Step 6: 20 m/s …

Card 3Position vector magnitude

Find the magnitude of the position vector of the point P(3, 4, 12).

Answer

Use the position vector magnitude formula: |OP| = √(x² + y² + z²) Step 1: Substitute x = 3, y = 4, z = 12. Step 2: |OP| = √(3² + 4² + 12²) Step 3: |OP| = √(9 + 16 + 144) = √169 Answer: |OP| = 13 units…

Card 4स्थिति सदिश का परिमाण

बिंदु P(3, 4, 12) के स्थिति सदिश का परिमाण ज्ञात कीजिए।

Answer

स्थिति सदिश के परिमाण का सूत्र उपयोग करें: |OP| = √(x² + y² + z²) चरण 1: x = 3, y = 4, z = 12 रखें। चरण 2: |OP| = √(3² + 4² + 12²) चरण 3: |OP| = √(9 + 16 + 144) = √169 उत्तर: |OP| = 13 units.

Card 5सदिश का अवयवी रूप

P(2, -5, 7) का स्थिति सदिश अवयव रूप में लिखिए और उसका परिमाण ज्ञात कीजिए।

Answer

चरण 1: स्थिति सदिश है r⃗ = xî + yĵ + zk̂. चरण 2: निर्देशांक रखिए: r⃗ = 2î - 5ĵ + 7k̂. चरण 3: परिमाण है |r⃗| = √(x² + y² + z²). चरण 4: |r⃗| = √(2² + (-5)² + 7²) = √(4 + 25 + 49) = √78. उत्तर: r⃗ = 2î -…

Card 6Component form of a vector

Write the position vector of P(2, -5, 7) in component form and find its magnitude.

Answer

Step 1: Position vector is r⃗ = xî + yĵ + zk̂. Step 2: Substitute coordinates: r⃗ = 2î - 5ĵ + 7k̂. Step 3: Magnitude is |r⃗| = √(x² + y² + z²). Step 4: |r⃗| = √(2² + (-5)² + 7²) = √(4 + 25 + 49) = √78…

Card 7Unit vector

Find the unit vector in the direction of a⃗ = 2î + 3ĵ + k̂.

Answer

Step 1: Find the magnitude first. |a⃗| = √(2² + 3² + 1²) = √14 Step 2: Use â = (1/|a⃗|)a⃗. Step 3: â = (1/√14)(2î + 3ĵ + k̂) Step 4: Write each component separately. Answer: â = (2/√14)î + (3/√14)ĵ + …

Card 8एकक सदिश

a⃗ = 2î + 3ĵ + k̂ की दिशा में एकक सदिश ज्ञात कीजिए।

Answer

चरण 1: पहले परिमाण ज्ञात कीजिए। |a⃗| = √(2² + 3² + 1²) = √14 चरण 2: â = (1/|a⃗|)a⃗ का उपयोग कीजिए। चरण 3: â = (1/√14)(2î + 3ĵ + k̂) चरण 4: प्रत्येक अवयव अलग-अलग लिखिए। उत्तर: â = (2/√14)î + (3/√14)ĵ +…

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Frequently Asked Questions

What are the important topics in Vector Algebra for Madhya Pradesh Board Class 12 Mathematics?
Key topics in Vector Algebra include A scalar has magnitude only, The vector from the origin O, If a vector makes angles α, A zero vector has coincident initial. Study these first, then practise questions on each for the Madhya Pradesh Board Class 12 board exam.
How many flashcards are available for Vector Algebra?
There are 52 flashcards for Vector Algebra covering key definitions, facts and ideas. A few sample cards are shown on this page.
How should I revise Vector Algebra for the Madhya Pradesh Board Class 12 board exam?
Learn the core ideas first, then work through the 117 practice questions on Vector Algebra. Revise definitions regularly and use flashcards for quick recall before the exam.

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