Mathbee CBSE Mathbee · CBSE Class 12 Maths
CBSE Class 12 Mathematics 2026 Main Paper 65(B) · Q303 Marksdot_products

CBSE Class 12 Mathematics 2026 Main Paper 65(B) · Question 30 (Vector Algebra)

For nonzero mutually perpendicular vectors a,b,c of equal norm, show that a+b+c is equally inclined to them.

✅ Step-by-Step Solution

Final Answer: Each cosine is 1/√3.
  1. Let each norm be m>0. The sum has squared norm 3m².
  2. Its dot product with each summand is m².
  3. Divide by the two norms to get the common cosine 1/√3.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Let each norm be m>0. The sum has squared norm 3m².
  • [2 marks] Its dot product with each summand is m².
  • [0.5 marks] Divide by the two norms to get the common cosine 1/√3.

Master Chapter 10: Vector Algebra

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Vector Algebra.
📘 Chapter Notes & All Exercises 🚀 Open Interactive Workspace →
← Previous Question
Evaluate \(\int_0^\pi x\,dx/(1+\sin x)\).
Next Question →
For feasible corners (0,10),(5,5),(15,15),(0,20), find p,q>0 such…

All Questions in CBSE Class 12 Mathematics 2026 Main Paper 65(B)

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38

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…