Question

The coordinates of the point where the line segment joining $A(5,1,6)$ and $B(3,4,1)$ crosses the yz plane are

• A. $(0,\frac{17}{2},\frac{13}{2})$
• B. $(0,-\frac{17}{2},\frac{13}{2})$
• C. $(0,\frac{17}{2},-\frac{13}{2})$
• D. $(0,-\frac{17}{2},-\frac{13}{2})$

Answer 1

The correct option is C $(0,\frac{17}{2},-\frac{13}{2})$

The direction ratios of line joining the points $(5,1,6)$ and $(3,4,1)$ are $2,-3,5$

Therefore the equation of line is $\frac{x-5}{2}=\frac{y-1}{-3}=\frac{z-6}{5}$

Given that the line crosses $yz$ plane . In $yz$ plane, $x=0$

$\Rightarrow \frac{0-5}{2}=\frac{y-1}{-3}=\frac{z-6}{5}$

$\Rightarrow y=\frac{17}{2},z=-\frac{13}{2}$

Therefore the correct option is $C$