Question

Find the ratio in which the plane 2x + 3y + 5z = 1 divides
the line joining the points (1, 0, -3) and (1, - 5,7).
T

Answer 1

Answer:

2:3

Step-by-step explanation:

Let r vector be the PV of the point of intersection of the plane & then line

Let the required ratio be a:1

Then, according to section formula:

r = [a(i - 5j + 7k) + 1(i - 3k)]/(a+1) = i(a+1)/(a+1) +j(-5a)/(a+1) + k(7a-3)/(a+1)

Replacing in the equation of the plane:

2(1) +3(-5a)/(a+1) +5(7a-3)(a+1) = 1

(-15a + 35a - 15) = -1(a+1)

20a - 15 = -a -1

21a = 14

a = 2/3