Question

The coordinates of the foot of the perpendicular drawn from the origin to the line joining the points $(-9,4,5)$ and $(10,0,-1)$ will be-

• A. $(-3,2,1)$
• B. $(1,2,2)$
• C. $(4,5,3)$
• D. None of these.

Answer 1

The correct option is D None of these.

Equation of line joining $(-9,4,5)$ and $(10,0,-1)$ is given by, $\frac{x+9}{-19}=\frac{y-4}{4}=\frac{z-5}{6}=k$ (say)
So any point on this line is given by, $P(-19k-9,4k+4,6k+5)$
Let origin is $O(0,0,0)$ so direction ratios of $PO$ are $-19k-9,4k+4,6k+5$
For $P$ to be foot of perpendicular from origin to this line,
$-19(-19k-9)+4(4k+4)+6(6k+5)=0$
$\Rightarrow k=\frac{-31}{59}$
Therefore, required point is $P(\frac{58}{59},\frac{112}{59},\frac{109}{59})$
Hence, option 'D' is correct.