Question
Question: Let A = (3, 5, 6) and B = (4, 6, -3). Find ratio in which YZ plane is dividing AB....
Let A = (3, 5, 6) and B = (4, 6, -3). Find ratio in which YZ plane is dividing AB.
A
3 : 4 externally
B
3 : 4 internally
C
4 : 3 externally
D
4 : 3 intern ± 4
Answer
3 : 4 externally
Explanation
Solution
We are given points
A = (3, 5, 6) and B = (4, 6, -3).
A point P on the line AB that lies on the YZ–plane must have x-coordinate 0. If we assume that P divides AB in the ratio k : 1, then by the section formula the x–coordinate of P is:
Pₓ = (k · Bₓ + Aₓ) / (k + 1) = (4k + 3) / (k + 1).
Setting Pₓ = 0 gives: (4k + 3) / (k + 1) = 0 ⟹ 4k + 3 = 0 ⟹ k = –3/4.
A negative value for k indicates that the division is external. In terms of ratio, the absolute values are used so the ratio is 3:4 externally.