Question

Coordinates of the foot of perpendicular from the point $(-1,2,4)$ on $z$-axis are

• A. $(-1,0,0)$
• B. $(-1,2,0)$
• C. $(0,0,4)$
• D. $(0,2,4)$

Answer 1

Answer: (C)

$(0,0,4)$

Given point is $P(-1,2,4)$
Any point on $z$-axis is given by $Q(0,0,k)$, where $k$ is any real number
So direction ratio of $PQ$ are $-1,2,4-k$
We know direction ratio of $z$-axis is given by $0,0,m$ (where $m$ is any non zero real number)
Now since $PQ\perp z$-axis
$\Rightarrow 0(-1)+0\left(2\right)+m(4-k)=0$

$\Rightarrow k=4$
Hence, coordinate of foot of perpendicular is $(0,0,4)$.