If z-coordinate of a point P on the line joining the points A (2, 2, 1) and B (5, 1, -2) is -1, then x-coordinate of point P is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4
Let P divide AB in the ratio k : 1. By the section formula, the coordinates of P are
\(\displaystyle \left(\frac{5k + 2}{k + 1},\ \frac{k + 2}{k + 1},\ \frac{-2k + 1}{k + 1}\right)\)
The z-coordinate is −1:
\(\displaystyle \frac{-2k + 1}{k + 1} = -1\)
\(-2k + 1 = -k - 1\)
\(k = 2\)
So the x-coordinate of P is
\(\displaystyle \frac{5(2) + 2}{2 + 1} = \frac{12}{3} = 4\)