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Ex 10.3, 7 - 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 10.3, 7 Evaluate the product (3𝑎 ⃗ − 5𝑏 ⃗) ⋅ (2𝑎 ⃗ + 7𝑏 ⃗). (3𝑎 ⃗ − 5𝑏 ⃗) ⋅ (2𝑎 ⃗ + 7𝑏 ⃗) = 3𝑎 ⃗ . 2𝑎 ⃗ + 3𝑎 ⃗.7𝑏 ⃗ − 5𝑏 ⃗.2𝑎 ⃗ − 5𝑏 ⃗. 7𝑏 ⃗ = 6(𝑎 ⃗. 𝑎 ⃗) + 21(𝑎 ⃗. 𝑏 ⃗) − 10 (𝒃 ⃗. 𝒂 ⃗) − 35 (𝑏 ⃗. 𝑏 ⃗) = 6(𝑎 ⃗. 𝑎 ⃗) + 21(𝑎 ⃗. 𝑏 ⃗) − 10 (𝒂 ⃗. 𝒃 ⃗) − 35 (𝑏 ⃗. 𝑏 ⃗) = 6(𝒂 ⃗. 𝒂 ⃗) + 11 (𝑎 ⃗. 𝑏 ⃗) −35 (𝒃 ⃗. 𝒃 ⃗) = 6 |𝒂 ⃗ |2 + 11(𝑎 ⃗. 𝑏 ⃗) − 35 |𝒃 ⃗ |2 Therefore, (3𝑎 ⃗ − 5𝑏 ⃗) ⋅ (2𝑎 ⃗ + 7𝑏 ⃗) = 6|𝒂 ⃗ |2 + 11 (𝒂 ⃗. 𝒃 ⃗) − 35 |𝒃 ⃗ |2
