How would I find the vector parametrization bbr(t) of the line L that passes through the points (2,1,4) and (5,6,7)?

Zoagliaj

Zoagliaj

Answered question

2022-07-21

Vector parametrization of the line that passes through two vectors.
How would I find the vector parametrization 𝐫 ( 𝑡 ) of the line L that passes through the points ( 2 , 1 , 4 ) and ( 5 , 6 , 7 )?
So I found a directional vector: ( 3 , 5 , 3 )
What do I do next?

Answer & Explanation

Jaycee Figueroa

Jaycee Figueroa

Beginner2022-07-22Added 10 answers

You found a direction vector ( 3 , 5 , 3 ) = ( 5 , 6 , 7 ) ( 2 , 1 , 4 )
so the line can be parametrized as ( 2 , 1 , 4 ) + t ( 3 , 5 , 3 ) = ( 2 + 3 t , 1 + 5 t , 4 + 3 t )
Note that r ( 0 ) = ( 2 , 1 , 4 ) and r ( 1 ) = ( 5 , 6 , 7 )

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