Question

If P $(3,2,-4)$ , Q $(5,4,-6)$ and R $(9,8,-10)$ are collinear, then R divides PQ in the ratio

• A. $3:2$ internally
• B. $3:2$ externally
• C. $2:1$ internally
• D. $2:1$ externally

Answer 1

The correct option is B $3:2$ externally

Let R divides PQ in ratio m:n.

By Section Formula

coordinates of R are:

$R=(\frac{5m+3n}{m+n},\frac{4m+2n}{m+n},\frac{-6m-4n}{m+n})$

we have coordinates of R=(9,8,-10)

Therefore,

$9=\frac{5m+3n}{m+n}$

$9m+9n=5m+3n$

$-6n=4m$

$\frac{m}{n}=\frac{-3}{2}$

Therefore R divides PQ in 3:2 ratio and negative sign indicates,it cuts Externally.

Therefore option (B) is Correct.