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Ex 10.4, 4 - Chapter 10 Class 12 Vector Algebra
Last updated at April 16, 2024 by Teachoo
Chapter 10 Class 12 Vector Algebra
Concept wise
- Scalar or vector
- Graphical displacement
- Type of vector
- Multiplication of a vector by a scalar
- Equal vectors
- Unit vector
- Direction cosines and ratios
- Addition(resultant) of vectors
- Joining two points
- Section formula
- Right Angled triangle
- Collinearity Of two vectors
- Collinearity of 3 points or 3 position vectors
- Scalar product - Defination
- Scalar product - Projection
- Scalar product - Solving
- Vector product - Defination
- Vector product - Area
-
Vector product - Solving
Transcript
Ex 10.4, 4 Show that (𝑎 ⃗ − 𝑏 ⃗) × (𝑎 ⃗ + 𝑏 ⃗) = 2(𝑎 ⃗ × 𝑏 ⃗) Solving L.H.S (𝑎 ⃗ − 𝑏 ⃗) × (𝑎 ⃗ + 𝑏 ⃗) = 𝑎 ⃗ × (𝑎 ⃗ + 𝑏 ⃗) − 𝑏 ⃗ × (𝑎 ⃗ + 𝑏 ⃗) = 𝑎 ⃗ × 𝑎 ⃗ + 𝑎 ⃗ × 𝑏 ⃗ − 𝒃 ⃗ × 𝒂 ⃗ − 𝑏 ⃗ × 𝑏 ⃗ = 𝑎 ⃗ × 𝑎 ⃗ + 𝑎 ⃗ × 𝑏 ⃗ − (− 𝒂 ⃗ × 𝒃 ⃗) − 𝑏 ⃗ × 𝑏 ⃗ = 𝑎 ⃗ × 𝑎 ⃗ + 𝑎 ⃗ × 𝑏 ⃗ + 𝑎 ⃗ × 𝑏 ⃗ − 𝑏 ⃗ × 𝑏 ⃗ = 𝒂 ⃗ × 𝒂 ⃗ + 2(𝑎 ⃗ × 𝑏 ⃗) − 𝒃 ⃗ × 𝒃 ⃗ 𝑎 ⃗ × 𝑎 ⃗ = |𝑎 ⃗ ||𝑎 ⃗ | sin θ 𝑛 ̂ = |𝑎 ⃗ |2 sin 0 𝑛 ̂ = 0 So, 𝑎 ⃗ × 𝑎 ⃗ = 0 Similarly, 𝑏 ⃗ × 𝑏 ⃗ = 0 = 0 + 2(𝑎 ⃗ × 𝑏 ⃗) − 0 = 2 (𝑎 ⃗ × 𝑏 ⃗) = RHS Since LHS = RHS, Hence proved.
