NCERT Class 12 · Ch 10 Exercise 10.3 · Q5
NCERT Class 12 Maths · Chapter 10 Vector Algebra · Exercise 10.3 Question 5
Show (2,3,6)/7, (3,−6,2)/7, (6,2,−3)/7 are unit vectors and mutually perpendicular.
💡 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: Each norm is 1; every pair has dot product 0.
- Their squared magnitudes are (4+9+36)/49, (9+36+4)/49 and (36+4+9)/49, all 1.
- The pairwise dot-product numerators are 6−18+12=0, 12+6−18=0, and 18−12−6=0. Dividing by 49 leaves zero.
Master Chapter 10: Vector Algebra
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Vector Algebra.
← Previous Question
Find the projection of…
Next Question →Find |a|,|b| if (a+b)·(a−b)=8 and |a|=8|b|.
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…