Question

Which of the follwing statements are correct ?
1. The coordinates of the point R which divides the line

segment joining two points $P(x_1,y_1,z_1)$ and $Q(x_2,y_2,z_2)$

externally in the ratio m:n are $(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n},\frac{m{z}_2+n{z}_1}{m+n})$.

2. If R divides PQ internally in the ratio m:n, then its coordinates

are obtained by replacing n by -n in the statement 1.

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

Answer 1

The correct option is D

None of these

1. The coordinates of the point R which divides the line segment

joining two points $P(x_1,y_1,z_1)$ and $Q(x_2,y_2,z_2)$ internally in

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

2. If the point R divides PQ externally in the ratio m:n, then its coordinates are obtained by replacing n by -n so that the

coordinates of point R will be $(\frac{m{x}_2-n{x}_1}{m-n},\frac{m{y}_2-n{y}_1}{m-n},\frac{m{z}_2-n{z}_1}{m-n})$

So,both the given statements are false.