If the points (−1, −1, 2), (2, m, 5) and (3, 11, 6) are collinear, then m equals
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 8
Let \(P(-1, -1, 2)\), \(Q(2, m, 5)\) and \(R(3, 11, 6)\). The points are collinear when \(\overrightarrow{PQ}\) and \(\overrightarrow{PR}\) are parallel, i.e. their components are proportional:
\(\overrightarrow{PQ} = (3,\ m + 1,\ 3)\)
\(\overrightarrow{PR} = (4,\ 12,\ 4)\)
The first and third components give the ratio \(\frac{3}{4}\), so
\( \displaystyle \frac{m + 1}{12} = \frac{3}{4} \)
\(m + 1 = 9,\quad m = 8\)
NCERT Exemplar:
Vector Algebra
