Question

The image of the point $(1,6,3)$ in the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ has the coordinates

• A. $(1,1,7)$
• B. $(0,1,7)$
• C. $(1,0,7)$
• D. None of these

Answer 1

The correct option is C $(1,0,7)$

The given point is $P(1,6,3)$
and line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}=k$(say) $.......\left(1\right)$
So any point on this line is given as$Q(k,2k+1,3k+2)$
Let Image of $P$ in the line (1) is $M$, so $PM$ will be perpendicular to the given line and $Q$ will be midpoint of $PM$.
Now direction ratios of $PQ$ are, $k-1,2k-5,3k-1$
Also $PQ\perp \left(1\right)$
$\Rightarrow 1(k-1)+2(2k-5)+3(3k-1)=0$
$\Rightarrow 14k-14=0\Rightarrow k=1$
Thus $Q=(1,3,5)$
Since $Q$ is the mid point of $PM$, therefore coordinate of $M$ is $(1,0,7)$
Hence, option 'C' is correct.