what? so dead...

[morning]

OC = i +2j -k
OD = 3i - j + k
M is the midpoint of CD
ON = 2NC
DN = (-7/3)i + (7/3)j - (5/3)k

DN intersect OM at P
if OP = OD + alphaDN
and OP = betaOM,

find alpha and beta???

so what i have done:
3i - j + k + alpha((-7/3)i + (7/3)j - (5/3)k) = beta(1/2CD)
3i - j + k + alpha((-7/3)i + (7/3)j - (5/3)k) = beta(1 - (3/2)j +k)

then i don't know what to do

[keltingmeith]

Welp, I haven't actually sat down to do it, but it looks like you can simply equate the components. This will give you a set of simultaneous equations which you can use to solve for alpha and beta.

[morning]

yes i equated the two equations, but then cause there is only one equation and two variables... i won't be able to solve it

[keltingmeith]

I can see that you equated the two equations - so now equate the COMPONENTS within the two equations.

For example, if:



Then for i:



Repeat this for j and k, and then you have 3 equations for 2 variables. So, pick the two nicer looking equations, and solve for alpha and beta.