CBSE Class 12 Mathematics 2026 Main Paper 65/1/1 · Question 14 (Vector Algebra)

✅ Step-by-Step Solution

1. Let P = −î−ĵ+2k̂, Q = 2î+mĵ+5k̂, R = 3î+11ĵ+6k̂.
2. Vector PQ = Q − P = (3, m+1, 3), vector PR = R − P = (4, 12, 4).
3. For collinearity, PQ × PR = 0. Computing the cross product gives components (4(m+1)−36, −(12−12), 36−4(m+1)) = (4m−32, 0, 32−4m).
4. Setting each component to zero: 4m−32=0 ⇒ m=8, and 32−4m=0 ⇒ m=8. Consistent.