If the points $(-1, -1, 2), (2, m, 5)$ and $(3, 11, 6)$ are collinear, then $m$ equals

8

The correct answer is Option (2) → 8

Given points: $P(-1,-1,2), Q(2,m,5), R(3,11,6)$

For collinearity: $\vec{PQ} = \lambda \vec{PR}$

Compute vectors:

$\vec{PQ} = (2 - (-1), m - (-1), 5 - 2) = (3, m+1, 3)$

$\vec{PR} = (3 - (-1), 11 - (-1), 6 - 2) = (4, 12, 4)$

Then $\vec{PQ} = k \vec{PR}$ for some $k$:

Compare components:

$3 = 4k \Rightarrow k = 3/4$

$m+1 = 12k = 12*(3/4) = 9 \Rightarrow m = 8$

$3 = 4k = 3$ (check) → consistent

Answer: $m = 8$