CBSE Class 12 Mathematics 2026 Main Paper 65/5/3 · Q293 Marksvector_collinearity
CBSE Class 12 Mathematics 2026 Main Paper 65/5/3 · Question 29 (Vector Algebra)
The points A=(55,−2), B=(5,8) and C=(a,−52) are collinear. Find a. OR For unit vectors a,b,c prove |a−b|²+|b−c|²+|c−a|²≤9.
Alternative 1 3 Marks
The points A=(55,−2), B=(5,8) and C=(a,−52) are collinear. Find a.
Answer: 305.
- Compute AB=(−50,10) and BC=(a−5,−60).
- Their second coordinates give BC=−6 AB.
- Match first coordinates: a−5=300.
Alternative 2 3 Marks
For unit vectors a,b,c prove |a−b|²+|b−c|²+|c−a|²≤9.
Answer: At most 9, with equality when a+b+c=0.
- Expand the squared differences to obtain 6−2(a·b+b·c+c·a).
- Also |a+b+c|²=3+2(a·b+b·c+c·a).
- Thus the sum is 9−|a+b+c|²≤9.