Question

Which of the following statments are correct?

1. The coordinates of the point which divides the line segment joining the points

$(1,-2,3)$ and $(3,4,-5)$ internally in the ratio $2:3$ is $(-3,-14,19)$.

2. The coordinates of the point which divides the line segment joining the points

$(1,-2,3)$ and $(3,4,-5)$ externally in the ratio $2:3$ is $(\frac{9}{5},\frac{2}{5},\frac{-1}{5})$.

• A. Only 1
• B. Only 2
• C. Both 1 & 2
• D. None of these

Answer 1

The correct option is D

None of these

(i) The coordinates of the point p which divides the line segment

joining two points $A(x_1,y_1,z_1)$ and $B(x_2,y_2,z_2)$ internally in the ratio m:n are

$(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n},\frac{m{z}_2+n{z}_1}{m+n})$.

Let P(x,y,z) be the point which divides line segment joining A(1,-2,3)

and B(3,4,-5) internally in the ratio 2:3 therefore,

$x=\frac{2\left(3\right)+3\left(1\right)}{2+3}=\frac{9}{5}$

$y=\frac{2\left(4\right)+3(-2)}{2+3}=\frac{2}{5}$

$z=\frac{2(-5)+3\left(3\right)}{2+3}=\frac{-1}{5}$

Thus,thecoordinate of the point p are $(\frac{9}{5},\frac{2}{5},\frac{-1}{5})$.

(ii)Let Q(x,y,z) be the point which divides line segment joining

$A(1,-2,3)$ and $B(3,4,-5)$ externally in the ratio $2:3$ is therefore,

Coordinates of point Q$(\frac{m{x}_2-n{x}_1}{m-n},\frac{m{y}_2-n{y}_1}{m-n},\frac{m{z}_2-n{z}_1}{m-n})$

$x=\frac{2\left(3\right)-3\left(1\right)}{2-3}=-3$

$y=\frac{2\left(4\right)-3(-2)}{2-3}=-14$

$z=\frac{2(-5)-3\left(3\right)}{2-3}=19$

Thus ,the coordinate of point Q is (-3,-14,19)

So, none of the statements are correct.