The points A(1, 2, 3), B(3, −1, 5) and C(7, k, 9) lie on a straight line. The value of k is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → −7
Three points are collinear when the direction ratios of AB and AC are proportional.
\(AB: 3-1, -1-2, 5-3 = 2, -3, 2\)
\(AC: 7-1, k-2, 9-3 = 6, k-2, 6\)
\( \displaystyle \frac{6}{2} = \frac{k-2}{-3} = \frac{6}{2} \)
\(k-2 = -9\)
\(k = -7\)