If z-coordinate of a point P on the line joining the points A(2, 2, 1) and B(5, 1, -2) is -1, than x-coordinate of point P is

4

The correct answer is Option (2) → 4

Given points: $A(2, 2, 1)$ and $B(5, 1, -2)$

Let point $P$ lie on the line segment joining $A$ and $B$.

Use section formula in parametric form:

General point on line joining $A$ and $B$ is:

$P = (1 - t)A + tB$

$x = (1 - t)(2) + t(5) = 2(1 - t) + 5t$

$y = (1 - t)(2) + t(1) = 2(1 - t) + t$

$z = (1 - t)(1) + t(-2) = 1 - t - 2t = 1 - 3t$

Given $z = -1$

$1 - 3t = -1 \Rightarrow 3t = 2 \Rightarrow t = \frac{2}{3}$

Substitute $t = \frac{2}{3}$ into $x$:

$x = 2(1 - \frac{2}{3}) + 5(\frac{2}{3}) = 2(\frac{1}{3}) + \frac{10}{3} = \frac{2}{3} + \frac{10}{3} = \frac{12}{3} = 4$