Mathbee CBSE Mathbee · CBSE Class 12 Maths
Class 12 Vector Algebra · Long Answer3 Marksdot_product_angle

Class 12 Maths · Vector Algebra · Long Answer #68

Nonzero mutually perpendicular vectors a,b,c have equal magnitudes. Prove a+b+c is equally inclined to each and find the common angle.

✅ Step-by-Step Solution

Final Answer: arccos(1/√3)
  1. Let their common magnitude be r>0 and s=a+b+c. Pairwise dot products vanish.
  2. Then |s|²=3r² and s·a=s·b=s·c=r².
  3. The cosine of each angle is r²/(r√3r)=1/√3.
  4. All three angles are arccos(1/√3), so the inclination is equal.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Let their common magnitude be r>0 and s=a+b+c. Pairwise dot products vanish.
  • [1 mark] Then |s|²=3r² and s·a=s·b=s·c=r².
  • [1 mark] The cosine of each angle is r²/(r√3r)=1/√3.
  • [0.5 marks] All three angles are arccos(1/√3), so the inclination is equal.

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
Given |a|=1, |b|=2, |c|=3, the scalar projections of b and c onto a…
Next Question →
For a=(1,1,1), b=(0,1,−1), find c such that a×c=b and a·c=3.

More Practice Questions in Vector Algebra

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38Q39Q40

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…