C4 Maths Question PLZ

Could you help with the last part of the question about ratios, thxs. I've got it rink up to the last bit.

Relative to a fixed origin, O, the line l has the equation
r = (i + pj − 5k) + λ(3i − j + qk),
where p and q are constants and λ is a scalar parameter.
Given that the point A with coordinates (−5, 9, −9) lies on l,
(a) find the values of p and q,
(b) show that the point B with coordinates (25, −1, 11) also lies on l.
The point C lies on l and is such that OC is perpendicular to l.
(c) Find the coordinates of C.
(d) Find the ratio AC : CB

Reply 1

Sinnoh

You just find the magnitudes of the two vectors and compare, right?

Reply 2

MiladA

Well

At A, lambda = -2
At B, lambda = 8
At C, lambda = 1

So the ratio is 3:7 (1- (-2)) : (8-1)

Reply 3

Chrispa

you find the distance of ac (x) and of cb (y) and divide by the smallest number to get a 1:? ratio or just put both numbers in the ratio and simlify x;y