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C4 - Simplifying Vector equation of the line!

Hi all, when creating a vector equation of the line which usually = a + λ(AB)

I'll give you an example:

a = 4i - j + k

b= 5i + j - k

So AB= i + 2j - 2k

and the vector equation:
r = 4i - j + k + λ(i + 2j - 2k)

In the next step I usually simplify it down again to get:

r = i(4 + λ) - j(1 + 2λ) + k(1 - 2λ)

But when having to find the position vector of that equation ^ with another one given in the paper I always end up getting the adverse sign to the correct answer!

So what my question is... when I do my extra simplifying step, must I keep the i's, j's and the k's adding each other as on my example above I have done "-j(1 + 2λ)".. should it be "+j(-1 + 2λ)" ?

Thanks to anyone who helps out!

Reply 1

TenOfThem

Original post by Ryan44

-j(1 + 2λ).. should it be +j(-1 + 2λ) ?

Well that particular bit should be -j(1 - 2λ)

Reply 2

TenOfThem

Original post by Ryan44

But when having to find the position vector of that equation ^ with another one given in the paper I always end up getting the adverse sign to the correct answer!