Question

If the plane a $2x-3y+5_Z-2=0$ divides the line segment joining $(1,2,3)$ and $(2,1,k)$ in the ratio $9:11$, then $k$ is

• A. $1$
• B. $-2$
• C. $-10$
• D. $-\frac{1}{2}$

Answer 1

The correct option is B $-2$

Coordinate of the point which divides the line segment joining the points $(1,2,3)$ and $(2,1,k)$ in the ratio $9:11$ are $(\frac{29}{20},\frac{31}{20},\frac{9k+33}{20})$

Also, this point will lie on the given plane

$\Rightarrow 2\times \frac{29}{20}-3\times \frac{31}{20}+5\times \frac{9k+33}{20}-2=0$

$\Rightarrow k=-2$

Hence, option B is correct.