Question

If the points $(h,3,-4),(0,-7,10)$ and $(1,k,3)$ are collinear, then $h+k$ is

• A. $4$
• B. $0$
• C. $-4$
• D. $14$

Answer 1

The correct option is B $0$

Any point lying on the line joining $(h,3,-4)$ and $(0,-7,10)$ can be written in the form of $(h-hl,3-10l,-4+14l)$, where $l$ is a constant.
Since, $(1,k,3)$ is also a point on this line, it should satisfy this form.
$\Rightarrow -4+14l=3$.

$\therefore l=$ $\frac{1}{2}$
$\Rightarrow k=3-10l=-2$
$\Rightarrow h(1-l)=1$

$\therefore h=2$
Hence, $h+k=2-2=0$