Question

If $R(a+2,a+3,a+4)$ divides the line segment joining $P(2,3,4)$ and $Q(4,5,6)$ in the ratio $-3:2$, then the value of the parameter which represents $a$ is

• A. $3$
• B. $2$
• C. $6$
• D. $-1$

Answer 1

The correct option is C $6$

If a point P divides the line segment joining $A=(x_1,y_1,z_1)$ and $B=(x_2,y_2,z_2)$ in the ratio $m:n$.

Then the point P is given by $(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n},\frac{m{z}_2+n{z}_1}{m+n})$.

In the given problem, we have

$a+2=\frac{-3\times 4+2\times 2}{-1}$.

On solving, we get $a=6.$