Thread: so confused, vector length exam tommorow!

given length BD is 15m and vector equation of line BD is

(-1) (15) i.e +lamda(15,-20,0)
(-7) + lamda (-20)
(11) (0)
find corordinates of D which is in mark scheme (8,-19,11)
This question is so easy but im so annoyed i cant understand it. I wouldnt have thought 15 comes from pythagarus of each point and someow thats incorporated, Obviously not as the mark scheme tells me to get lamda as 3 or 3/5 as appropriate(HOW) then sub in! where does lamda come from....????

Originally Posted by i_zz_y_ill

given length BD is 15m and vector equation of line BD is

(-1) (15) i.e +lamda(15,-20,0)
(-7) + lamda (-20)
(11) (0)
find corordinates of D which is in mark scheme (8,-19,11)
This question is so easy but im so annoyed i cant understand it. I wouldnt have thought 15 comes from pythagarus of each point and someow thats incorporated, Obviously not as the mark scheme tells me to get lamda as 3 or 3/5 as appropriate(HOW) then sub in! where does lamda come from....????

The equation of a line is written as:

. So you get:


Instead of t some authors prefer

Obviously B(-1, -7, 11) and the direction vector is

So you can calculate the coordinates of D by:



Now calculate

The length of

Solve for and you'll get:

Plug in this value into the equation of the line to calculate the coordinates of D:

or