NCERT Class 12 · Ch 10 Exercise 10.4 · Q7
NCERT Class 12 Maths · Chapter 10 Vector Algebra · Exercise 10.4 Question 7
For component vectors a=(a₁,a₂,a₃), b=(b₁,b₂,b₃), c=(c₁,c₂,c₃), prove a×(b+c)=a×b+a×c.
💡 Concept Hints
- Write the vector components and identify the required direction or geometric relation.
- Use the magnitude, dot-product, cross-product or section formula that matches the requested quantity.
✅ Step-by-Step Solution
Final Answer: The cross product distributes over addition.
- The first component on the left is a₂(b₃+c₃)−a₃(b₂+c₂)=(a₂b₃−a₃b₂)+(a₂c₃−a₃c₂).
- The other two components similarly become (a₃b₁−a₁b₃)+(a₃c₁−a₁c₃) and (a₁b₂−a₂b₁)+(a₁c₂−a₂c₁). These are exactly the components on the right.
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