Mathbee · CBSE Class 12 Maths

CBSE Class 12 Mathematics 2026 Main Paper 65/2/2 · Q222 Marksvector_median

CBSE Class 12 Mathematics 2026 Main Paper 65/2/2 · Question 22 (Vector Algebra)

For AB=(0,1,1) and AC=(3,−1,4), prove AD=(AB+AC)/2 where D is the midpoint of BC, then find |AD|.

Triangle ABC drawn to scale in its plane. D is halfway along BC and AD is the median.

✅ Step-by-Step Solution

Final Answer: AD=(3/2,0,5/2), length √34/2.

Use AD=AB+BD and BD=BC/2.
As BC=AC−AB, this gives AD=(AB+AC)/2=(3,0,5)/2.
The length is √34/2.

📋 CBSE Stepwise Marking Scheme

[0.5 marks] Use AD=AB+BD and BD=BC/2.
[1 mark] As BC=AC−AB, this gives AD=(AB+AC)/2=(3,0,5)/2.
[0.5 marks] The length is √34/2.

Master Chapter 10: Vector Algebra

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Vector Algebra.

📘 Chapter Notes & All Exercises 🚀 Open in Interactive Workspace →

← Previous Question

Find the absolute maximum of cos x+sin²x on [0,π]. OR The volume of…

Next Question →

Find the foot from the origin to x=(y+1)/(−1)=(z−3)/(−2).

All Questions in CBSE Class 12 Mathematics 2026 Main Paper 65/2/2

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q24 Q25 Q26 Q27 Q28 Q29 Q30 Q31 Q32 Q33 Q34 Q35 Q36 Q37 Q38

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…