Finding a third equation that generates the same line
From the given the given data it is said that the two vectors are scalar multiples of each other.two vectors are parallel when direction vectors scalar multiple of each other
when t=2 the first equation
when t=0 the second equation
therefore the two lines are coincident lines.
lets consider first equation
substituting t=t'+2
solving this for t=0 gives the point
Writing two other equations that gives the same line
lets consider first equation
substituting t=2t'+2 gives
substituting t=3t'+2 to the first equation gives
and for both of them, the direction vector is a scalar multiple of each other
Since the lines are coincident and parallel the lines are as shown in the following figure ,where for various t values the lines follow the vector shown in the figure.
Comments
Leave a comment