Given: P(3, 2, -4), Q(5, 4, -6) and R(9, 8, -10) and P, Q and R are collinear
To find: the ratio in which Q divides PR
Formula used:
Section Formula:
A line AB is divided by C in m:n where A(x, y, z) and B(a, b, c).
The coordinates of C is given by,
\(\Big(\frac{nx+ma}{m+n},\frac{ny+mb}{m+n},\frac{nz+mc}{m+n}\Big)\)
Let Q divides PR in ratio k : 1
Therefore, m = k and n = 1
P(3, 2, -4), Q(5, 4, -6) and R(9, 8, -10)
Coordinates of Q using section formula:
On comparing:
\(\frac{9k+3}{k+1}\) = 5
⇒ 9k + 3 = 5(k + 1)
⇒ 9k + 3 = 5k + 5
⇒ 9k – 5k = 5 – 3
⇒ 4k = 2
⇒ k = \(\frac{2}{4}\)
⇒ k = \(\frac{1}{2}\)
Q divides PR externally in ratio 1:2
