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CBSE Class 12 Mathematics 2026 Main Paper 65/2/3 · Q252 Marksvector_median

CBSE Class 12 Mathematics 2026 Main Paper 65/2/3 · Question 25 (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.

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