Question

A point $P$ lies on a line whose ends are $A(1,2,3)$ and $B(2,10,1).$ If $z$ component of $P$ is $7,$ then the coordinates of $P$ are

• A. $(-1,-14,7)$
• B. $(1,-14,7)$
• C. $(-1,14,7)$
• D. $(1,14,7)$

Answer 1

Answer: (A)

$(-1,-14,7)$

The equation of line passing through $A$ and $B$ is $\frac{x-1}{2-1}=\frac{y-2}{10-2}=\frac{z-3}{1-3}\Rightarrow \frac{x-1}{1}=\frac{y-2}{8}=\frac{z-3}{-2}=r$

Substitute $z=7$, we get

$\Rightarrow \frac{x-1}{1}=\frac{y-2}{8}=\frac{7-3}{-2}=-2$

Solve it to get $x=1-2=-1$, $y=2-16=-14$

So $P:$ $(-1,-14,7)$