Question

The coordinates of a point which divide the line joining the points $P(2,3,1)$ and $Q(5,0,4)$ in the ratio $1:2$ are

• A. $(\frac{7}{5},1,\frac{5}{3})$
• B. $(4,1,3)$
• C. $(3,2,2)$
• D. $(1,-1,1)$

Answer 1

The correct option is C $(3,2,2)$

Assume the coordinate of $R$ be $(x,y,z)$ that divides the line joining $P$ and $Q$ in the ratio of $1:2$
Therefore coordinate of $R$
$R(x,y,z)$$=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+m{y}_1}{m+n},\frac{m{z}_2+n{z}_1}{m+n})=(\frac{1\left(5\right)+2\left(2\right)}{1+2},\frac{1\left(0\right)+2\left(3\right)}{1+2},\frac{1\left(4\right)+2\left(1\right)}{1+2})=(\frac{9}{3},\frac{6}{3},\frac{6}{3})=(3,2,2)$