Question

The point collinear with $(1,–2,–3)$ and $(2,0,0)$ among the following is?

• A. $(0,4,6)$
• B. $(0,–4,–5)$
• C. $(0,–4,–6)$
• D. $(0,–4,6)$

Answer 1

The correct option is C

$(0,–4,–6)$

Find the collinear point

Given, two points $(1,–2,–3)$ and $(2,0,0)$

Any point lying on the joining $(1,–2,–3)$ and can be written in the from of

$\left(1+k,-2+2k,-3+3k\right)$

Since, all the options have their $x$-coordinate as $0$

$$\begin{gathered} \therefore 1+k=0 \\ \Rightarrow k=-1 \end{gathered}$$

So, $y=-2+2k$

$$\begin{gathered} y=-2+2(-1) \\ y=-4 \end{gathered}$$ $[k=-1]$

and $z=-3+3k$

$$\begin{gathered} z=-3+3(-1) \\ z=-6 \end{gathered}$$

Therefore, the point is $(0,-4,-6)$

Hence, option (C) is the correct answer.