Question

Coordinates of the foot of perpendicular from the point $(-2,5,4)$ on $y$-axis are

• A. $(-2,0,0)$
• B. $(0,5,0)$
• C. $(-2,0,4)$
• D. $(0,-5,0)$

Answer 1

Answer: (B)

$(0,5,0)$

Given point is $P(-2,5,4)$
Any point on $y$-axis is given by $Q(0,k,0)$, where $k$ is any real number
So direction ratio of $PQ$ are $-2,5-k,4$
We know direction ratio of $y$-axis is given by $0,m,0$ (where $m$ is any non zero real number)
Now since $PQ\perp y$-axis
$\Rightarrow 0(-2)+m(5-k)+0\left(4\right)=0$

$\Rightarrow k=5$
Hence, coordinate of foot of perpendicular is $(0,5,0)$.