3d vectors. Does a point lie on the line?

1. The problem statement, all variables and given/known data

L1 has the vector equation r=2i+3j-5k + t(4i-2j+k)
Does the point (16,-3,-2) lie on the line?

2. Relevant equations

Unknown

3. The attempt at a solution

I have a simple(i think) vector question but i just don't know the method to work it out.


I have searched on the internet and through my books and i can't find a similar problem anywhere. Any help would be much appreciated.

Thanks
 
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The point (16, -3, -2) can also be written as 16i - 3j - 2k. Does that help? Try writing the line in the similar form r = Ai + Bj + Ck where A, B, and C may be functions of t.
 
Last edited:

HallsofIvy

Science Advisor
41,626
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Conversely, the vector equation for the line r=2i+3j-5k + t(4i-2j+k) is the same as the parametric equation x= 2+ 4t, y= 3- 2t, z= -5+ k.
 

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