How do you write a vector equation and a parametric equation for each line: the line through A ( − 1 , 2 , 1 ) and B ( 1 , 2 , 1 )?

Question

How do you write a vector equation and a parametric equation for each line: the line through   A  (  −  1  ,     2  ,     1  ) and   B  (  1  ,     2  ,     1  )?

1s1zubv · Accepted Answer

Step 1The vector equation of a line involves a point on the line and the vector direction of the line.So using point   A  (  −  1  ,     2  ,     1  ) and direction                     A        B            →      we get a line with vector equation      r          (      λ      )        =    A    +    λ    ⋅                  A        B            →            r          (      λ      )        =          (      -      1      ,      2      ,      1      )        +    λ          (              (        1        ,        2        ,        1        )            -              (        -        1        ,        2        ,        1        )            )            r          (      λ      )        =          (      -      1      ,      2      ,      1      )        +    λ          (      2      ,      0      ,      0      )      To parametrically define this line we now take each component (x,y,z) or (i,j,k) individually      x    =    -    1    +    2    λ    r  (  t  )  =  y  =  2      z    =    1

How do you write a vector equation and a parametric equation for each line: the line through A

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