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

rjawbreakerca

rjawbreakerca

Answered

2022-07-05

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 )?

Answer & Explanation

1s1zubv

1s1zubv

Expert

2022-07-06Added 17 answers

Step 1
The 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

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