Question

If$A(1,2,-1)andB(-1,0,1)$ are given, then the co-ordinates of $P$ which divides $AB$ externally in the ratio $1:2$ are

• A. $(1,4,–1)$
• B. $(3,4,–3)$
• C. $\frac{1}{3}(3,4,–3)$
• D. $Noneofthese$

Answer 1

The correct option is B

$(3,4,–3)$

Explanation for correct option:

Finding coordinates:

If a point P$(x,y,z)$ is externally divide the line in the ration $m:n$then the coordinate of point is given by

$x=\frac{m{x}_1-n{x}_2}{m-n},y=\frac{m{y}_1-n{y}_2}{m-n},z=\frac{m{z}_1-n{z}_2}{m-n}$

Here, $$\begin{gathered} x_1=1,y_1=2,z_1=-1\&x_2=-1,y_2=0,z_2=1 \\ m:n=1:2 \end{gathered}$$

Now put the value in the above equation

$\begin{array}{rcl}x& =& \frac{2\times 1-1\times (-1)}{2-1},y=\frac{2\times 2-1\times 0}{2-1},z=\frac{-1\times 2-1\times 1}{2-1}\\ x& =& 3,y=4,z=-3\\ & & Pointsare(3,4,-3)\end{array}$

Hence, correct option is $\mathbf{\left(}\mathit{B}\mathbf{\right)}$.