NCERT Class 12 · Ch 10 Exercise 10.3 · Q13
NCERT Class 12 Maths · Chapter 10 Vector Algebra · Exercise 10.3 Question 13
Unit vectors a,b,c satisfy a+b+c=0. Find a·b+b·c+c·a.
💡 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: −3/2.
- Take the squared magnitude: 0=|a+b+c|²=|a|²+|b|²+|c|²+2(a·b+b·c+c·a).
- The three squared norms total 3, so the required sum is −3/2.
Master Chapter 10: Vector Algebra
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Vector Algebra.
← Previous Question
If a·a=0 and a·b=0, what follows about b?
Next Question →A zero factor gives a·b=0. Show the converse need not hold.
Related Questions in Vector Algebra
Class 12 Vector Algebra · Mcq Single Correct
Find |a × b|² + (a · b)².
Class 12 Vector Algebra · Mcq Single Correct
Find the area of triangle OAB, where OA = (1,2,3) and OB = (−3,−2,1).
Class 12 Vector Algebra · Mcq Single Correct
For nonzero vectors a,b with angle θ ∈ [0,π], when is a · b ≥ 0?
Class 12 Vector Algebra · Mcq Single Correct
For a vector a, find (a · i)i + (a · j)j + (a · k)k.
Class 12 Vector Algebra · Mcq Single Correct
Which vector has magnitude 9 and the same direction as (1,−2,2)?
Class 12 Vector Algebra · Mcq Single Correct
Find the position vector dividing the segment from 2a − 3b to a + b internally in the ratio…