Vector equation of a line: points A(5,1,2) and B(-1,7,8)

[Monkeyseat]

Hi,

Question

The points A(5, 1, 2) and B(-1, 7, 8) have position vectors a and b, respectively.

a) Show that the two lines r = a + s(4i - j + k) and r = b + t(2i - 5j - 7k) intersect and find the coordinates of the point of intersection C.
b) Find a vector equation of AB.

Working

a) I got the correct answer for this part.

b) For this, I got:

r = 5i + j + 2k + s(-6i + 6j + 6k)

The book got:

r = 5i + j + 2k + s(i - j - k)

If the book is correct, how did they get this answer?

Thanks.

 

[tkhunny]

Re: Vector equation of a line

It's called "simplified". In your stude of vectors, you should have encountered the concept that stretching a line doesn't make it a different line.

Factor out "-6" from yours. (-6s)(i-j-k)

Looks rather similar, doesn't it?